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Mo. 


TEACHERS'  MANUAL 


—FOR  — 


Andrews'  Lunar  Tellurian 


BY 

HOWARD    H.    GROSS. 


Second    Edition. 

PUBLISHED  BY 

A.  H.  ANDREWS  &  Co., 
CHICAGO. 

1882. 


Copyrighted  by 

HOWARD  H.  GROSS, 

CHICAGO,  iSSi. 


Introduction. 


To  THE  TEACHER  : 

In  the  preparation  of  this  Manual  the  writer  has  endeavored  to 
treat  the  subjects  presented,  in  a  simple  yet  forcible  manner,  avoid- 
ing, as  much  as  possible,  technical  terms.  The  illustrations  given,  ' 
outline  the  work  that  should  be  done  in  the  class-room.  The 
teacher  should,  and  no  doubt  will  supplement  these  illustrations 
in  many  ways,  presenting  the  subjects  treated,  step  by  step,  in  a 
thorough  and  yet  attractive  manner. 

The  value  of  demonstration  is  no  longer  doubted,  and  in  those  - 
schools  where  it  is  most  used  the  best  results  follow.  This  is 
pre-eminently  true  in  geographical  and  astronomical  work.  The 
Lunar  Tellurian  is  designed  to  furnish  the  illustrations  necessary 
to  give  the  pupils  a  comprehensive  understanding  of  the  relation- 
ships of  the  earth,  sun  and  moon.  It  is  so  simple  in  construction 
that  the  average  teacher  may  use  it  to  advantage  after  a  few 
hours'  study  with  the  Manual.  < 

The  teacher  will  find  it  advantageous  to  now  and  then  assign  a 
topic  to  one  of  the  pupils,  and  require  him  to  furnish  clear  and 
forcible  demonstrations  by  use  of  the  apparatus. 

The  teacher's  attention  is  particularly  called  to  the  section  in 
which  Prof.  E.  Colbert,  now  scientific  editor  of  the  Chicago 
Tribune,  and  well  known  as  a  practical  astronomer,  treats  the 
subject  of  Tides.  His  presentation  is  new,  having  reduced  the 
abstract  to  the  concrete.  The  author  congratulates  the  readers 
upon  being  able  to  present  an  article  from  the  pen  of  Prof.  Colbert, 
and  here  acknowledges  obligations  to  that  estimable  and  scholarly 
gentleman. 

The  writer  acknowledges  his  obligations  to  M.  MacVicar,  Ph. 
D.,  of  the  Michigan  State  Normal  School — than  whom  there  is 
no  better  authority  on  mathematical  geography — some  of  whose 
illustrations  the  writer  has  embodied  in  this  work. 

CHICAGO,  March  i,  iSSi. 


111861 


NDEX 


Introduction,            •  j 

Andrews'  Lunar  Tellurian,  Description,            -  •               3 

How  to  Adjust  the  Lunar  Tellurian,            -  -                     6 

Preparatory   Work,                                       ...  ^ 

General  Definitions,  -                      8-16 

Distribution  of  Light  and  Heat,             -  -             16-24 

Days  and  Nights  :    Equal  and  Unequal,  -                 24-27 

The  Sun's  Apparent  Path,  27-28 

Change  of  Season,  28-30 

Twilights,  3o-33 

The  Sun's  Declination,  34 

To  find  the  Latitude  and  Longitude  oj  Places,  35 

Longitude  and  Time,                                           -  37~39 
To  find  the  Difference  of  Longitude  between   Two 

Places,  39-41 

To  find  the  Time  of  Sunrise  and  the  Length  of  Twilight,  41 

The  Sun,                                                               -  42—43 

The  Earth,  44-45 

The  Moon,                         •  45-46 

The  Moon's  Motions,  Phases,  Etc.,  -         46-55 

The  Zodiac,  Signs  of,  Etc.,        -  55~59 

Eclipses,  Solar  and  Lunar,            -             -  -          59~68 

Precession  of  the  Equinoxes,  •             -         68—70 

Equation  of  Time,  7°~74 

The  Tides.— By  PROF.  COLBERT,  74~79 

Commendations  of  Andrews'  Lunar  Tellurian,  80 

4 


Andrews'  Lunar  Tellurian. 


A.  The  globe  balL  S.  Arc  of  the  sun's  circumference,  drawn 
upon  the  same  scale  as  the  globe.  Extend  the  arc  S  until  a  circle 
is  completed,  and  this  circle  shows  the  size  of  sun  upon  the  same 
scale  as  the  globe  represents  the  earth.  B.  The  circle  of  illu- 
mination, showing  how  far  the  sunlight  extends.  C.  The  twilight 
circle  showing  how  far  the  twilight  extends.  D.  The  moon  ball, 
showing  the  light  and  dark  hemispheres  of  the  moon.  The  gear- 
ing at  F  keeps  the  light  hemisphere  always  toward  the  sun.  E. 
Plate  showing  the  inclinatian  of  the  moon's  orbit.  G.  A  calen- 
dar index.  L.  Pointer  showing  the  position  of  the  sun's  vertical 
ray.  H.  A  longitudinal  or  time  index,  used  to  find  time  of  sun- 
rise and  sunset,  length  of  days,  nights  and  twilight.  J.  The 
ecliptic.  K.  The  equator. 


LUNAR  TELLURIAN  MANUAL. 


To  Adjust  the  Lunar  Tellurian. 

To  adjust  the  apparatus  to  agree  with  the  calendar, 
move  the  arm  IX  until  the  calendar  index  G  is  opposite 
the  21st  of  June  ;  place  the  arm  in  which  the  south  pole 
of  the  globe  is  fastened  parallel  with  the  arm  IX,  as 
shown  in  cut,  or  bring  the  calendar  index  to  June  21st 
and  place  the  center  of  the  socket  at  the  south  pole  op- 
posite the  mark  I  on  the  semi-circular  brace  joining  the 
ends  of  circle  C.  The  pointer  L  should  be  parallel  with 
the  arm  IX. 

Raise  the  moon  ball  until  the  gear  wheels  at  F  are 
disengaged,  turn  the  cog-wheel  to  the  right  or  left  until 
the  white  side  of  the  moon  ball  is  toward  the  sun,  drop 
the  cogs  into  gear.  The  gearing  will  keep  the  bright 
side  of  the  moon  ball  toward  the  arc  S. 

The  apparatus  is  now  fully  adjusted  for  use. 


For  Geographical  Study. 

(The  Globe  may  be  used  for  geographical  purposes  and  is  an 
excellent  one  for  such  use,  having  the  Isothermal  Lines  indicated 
in  blue  and  red.  The  ocean  currents  are  also  shown.  When  thus 
used,  the  teacher  will  remove  the  circles  B  C,  also  the  curved 
standards  supporting  the  same  (after  lifting  off  the  globe  ball 
along  with  the  axis.)  Replace  the  globe,  detach  the  moon  also, 
at  F,  by  tipping  the  ball  toward  the  globe.  The  sun  arc  S,  may 
also  be  removed.  All  these  changes  take  but  a  moment,  giving 
an  unobstructed  view  of  the  Globe.) 


LUNAR  TELLURIAN  MANUAL. 


Preparatory  Work. 

The  study  of  the  method  of  adjusting  and  handling 
the  LUNAR  TELLURIAN  GLOBE  in  illustrating 
and  solving  problems. 

Before  using  the  globe  in  illustrations,  the  following 
points  should  be  carefully  studied.  Each  adjustment 
should  be  made  familiar  by  actual  practice.  The  teacher 
cannot  be  too  particular  on  this  point,  as  the  power  of 
any  illustration  depends  largely  upon  the  tact  with  which 
the  piece  of  apparatus  used  is  handled. 

The  cut  on  the  preceding  page  represents  the  globe 
with  all  the  attachments  in  position.  Let  every  part  be 
removed  and  replaced  and  set  in  the  positions  indicated 
again  and  again,  until  everything  required  can  be  done 
with  ease  and  rapidity. 

Be  particular  to  notice  the  following  suggestions  : 

1.  The  arc  6*  represents  the  curvature  of  the   surface 
of  a  ball  which  bears  the  same  relation  in  size  to  the  sun 
that  the  globe  A  bears  to  the  earth.     Hence  by  com- 
pleting the  circle  of  which  the  arc  61  is  a  part,  and  com- 
paring it  with  a  great  circle  on  the  globe,  we  have  a 
correct  representation  of  the  relative   size  of  the   earth 
and  sun. 

2.  The  pointer  L    represents    a   line  connecting  the 
center  of  the  earth  and  sun,  hence,  indicates  the  position 
of  the  only  vertical  ray  of  light  or  heat  which   comes 
from  the  sun  to  the  earth. 

3.  The  circle  B  is  used  to  indicate  the  line  which  sep- 
arates light  from   darkness  ;  hence  is  called  the  "  Circle 
of  Illumination,"  or  "  Day  and  Night  Circle." 


LUNAR  TELLURIAN  MANUAL. 


General  Definitions. 

The  following  definitions  should   be    made    familiar 
before  commencing  the  use  of  the  globe. 

1.  A  Point  is  that  which  has  position  without  mag- 
nitude. 

2.  A  Line  is  the  path  of  a  moving  point. 

3.  A  Straight  Line  is  one  which  has  the  same  di- 
rection throughout  its  entire  length. 

4.  A  Curved  Line  is  one  which  changes  its  direc- 
tion at  every  point. 

5.  Parallel  Lines  are  lines  which  have  the  same 
direction. 

6.  An  Angle  is  the  opening  between  two  lines  which 
meet  in  a  common  point  called  a  vertex. 

There  are  three  kinds  of  angles,  thus  : 

(1)  (2)  (3)  (4) 


HORIZONTAL* 

Two  Eight  Angles,       One  Eight  Angle.        Obtuse  Angle.        Acute  Angle. 

7«  When    a   line   meets   another  line,  making,  as   is 

shown    (in  1),  two  equal  angles,  each  angle  is  a  Right 

Angle,  and   the    lines    are  said  to  be  perpendicular  to 

each  other. 

8.  An  Obtuse  Angle  is  an  angle  (as  shown  in  6 — 
3),  that  is  greater  than  a  right  angle. 

9.  An  Acute  Angle  is   an  angle  (as  shown  in  6 — 
4),  that  is   less  than  a  right  ang-le. 


LUNAR  TELLURIAN  MANUAL. 


10.  A  Plane  is  a  szirface   traced  by   a  straight  line 
moving  in  the  same  direction. 

11.  A  Circle  is  a  surface 
enclosed  by   a   curved  line, 

%*  every  point  of  which  is 
equally  distant  from  a  point 
within  called  the  center. 

1 2.  A  Circumference 

is  the  line  that  bounds  the 
circle. 

In  describing  the  lines  on 
the  sm-face  of  the  globe,  the 
word  circle  is  used  in  place  of  circumference.  When  a 
circle  proper  is  intended,  the  word  "plane"  is  introduced. 

13.  A    Degree  is  one  of  the    360  equal  parts  into 
which  the  circumference  of  a  circle  is  supposed  to  be 
divided. 

Observe,  the  length  of  a  degree  varies  with  the  size  of 
the  circle. 

14.  The  Diameter  of  a  circle  is  a  straight  line  pass- 
ing through  its  center  and  terminating  at  both  ends  in 
the  circumference. 

15.  The  Radius  of  a  circle  is  any  straight  line  ex- 
tending from  its  center  to  the  circumference. 

16.  A  Sphere  is   a  solid  or   volume  bounded  by  a 
curved  surface,  such  that  all   points  in  it  are  equally  dis- 
tant from  a  point  within  called  the  center. 


io  LUNAR  TELLURIAN  MANUAL. 

Observe  the  point  e.  in  the 
cut  in  the  margin,  is  the  center 
of  a  sphere  of  which  c  b  d  is 
the  lower  half. 

17.  The  Diameter  of  a 

sphere  is  a  straight  line  passing 
through  its  center  and  termin- 
ating at  both  ends  in  the  sur- 
face. 

In  the  cut,  ab  and  cd  are  diameters. 

18.  The  Radius  of  a  sphere  is  a  straight  line  drawn 
from  the  center  to  any  point  in  the  surface. 

In  the  cut,  ce,  fe,  ae^  ge  and  de  are  radii. 

19.  A  Great  Circle  of  a  sphere  is  one  whose  plane 
passes  through  the  center  of  the  sphere. 

Hence  the  planes  of  all  great  circles  divide  the  sphere 
into  two  equal  parts.     Each  part  is  called  a  Hemisphere. 

20.  A  Small  Circle  of  a  sphere  is  one  whose  plane 
does  not  pass  through  the  center  of  the  sphere. 

Hence,  the  planes  of  all  small  circles  on  a  sphere  di- 
vide the  sphere  into  two  unequal  parts. 

21.  The  Axis  of  the    Earth    is  that  diameter   on 
which  it  rotates  once  in  twenty-four  hours. 

22.  The  Poles  of  the  Earth  are  the  two  points  on 
its  surface  at  the  extremities  of  its  axis. 

23.  The  North   Pole  is  the  Pole  directed  to  the 
North  Star.     The  South  Pole  is  the  opposite  extrem- 
ity of  the  axis. 


LUNAR  TELLURIAN  MANUAL. 


24.  The  Equator  is  a  great  circle  midway  between 
the  poles  whose  plane  is  at  right  angles  to  the  axis  of  the 
earth. 

25.  The  Parallels  of  Latitude  are  small  circles 
parallel  to  the  Equator. 

26.  A  Meridian  is  a   semi-circle   extending   from 
Pole  to  Pole. 

27.  The  Latitude  of  a  place  is  its  distance  in  de- 
grees north  or  south  of  the  Equator. 

Places  north  of  the  Equator  are  said  to  be  in  North 
Latitude,  and  places  south  in  South  Latitude. 

28.  The  Longitude  of  a  place  is  its  distance  in  de- 
grees east  or  west  of  a  given  meridian  called  the  First 
or  Prime  Meridian. 

The  meridian  of  the  Royal  Observatory  at  Greenwich, 
England,  is  commonly  employed  as  the  Prime  Merid- 
ian. The  French  use  the  meridian  of  Paris  ;  the  Ger- 
mans that  of  Ferro,  one  of  the  Canary  Islands  ;  and 
Americans  frequently  use  that  of  Washington. 

29.  The  Tropic  of  Cancer  is  a  parallel  of  latitude 
23 1^  degrees  north  of  the  Equator. 

30.  The  Tropic  of  Capricorn  is  a  parallel  of  lati- 
tude 23  ^  degrees  south  of  the  Equator. 

31.  The  Orbit  of  the  Earth  is  the  path  in  which  it 
moves  round  the  sun. 

Observe,  the  plane  of  the  earths  orbit  is  the  plane  in 
which  the  orbit  is  described. 


12  LUNAR  TELLURIAN  MANUAL. 

32.  The  Zones  are  broad  belts  or  divisions  of  the 
earth's  surface  bounded  by  the  Tropics  and  Polar  Circles. 

These  four  lines  divide  the  surface  of  the  earth  into  five 
zones  or  belts  known  as  the  Torrid  Zone,  the  two  Tem- 
perate Zones,  and  the  two  Frigid  Zones. 

The  width  of  the  Zones  depends  entirely  upon  the  in- 
clination of  the  axis.  The  width  of  the  Torrid  Zone  is 
double  the  inclination  of  the  axis  (23^  degrees),  or  47 
degrees.  The  width  of  the  Frigid  Zone  is  equal  to  the 
inclination.  The  Temperate  Zones  embrace  whatever 
surface  lies  between  the  Tropics  and  Polar  Circles  (43 
degrees).  If  the  inclination  of  the  axis  were  30  degrees? 
as  in  the  case  of  the  planet  Saturn,  the  Zones  would  be 
as  follows  : 

Torrid  Zone,  double  the  inclination,  30°  or  60° 

Frigid  Zones,  each  equal  to  the  inclination,  30°  or  60° 
Temp.  Zones,  each  equal  to  the  inclination,  30°  or  60° 

Total  degrees  from  pole  to  pole,  180° 

33.  The  Ecliptic  is  the  sun's  apparent  yearly  path 
through  the   fixed  stars,  or  the  earth' }s  real  path  or  orbit. 

34.  The    Zodiac  is  a  belt  of  the  heavens  16  degrees 
wide,  lying  8  degrees  on  each  side  of  the  Ecliptic,  within 
which  the  sun,  moon  and  planets  are  seen  to  move. 

This  belt  is  divided  into  twelve  equal  parts  called 
Signs  of  the  Zodiac,  These  divisions,  with  their  names, 
are  represented  on  the  base  of  the  Lunar  Tellurian. 

35.  The  Equinoctial  or  Celestial  Equator  is 

a  great  circle  of  the  Celestial  Sphere  directly  over  the 
terrestrial  equator,  and  hence  is  in  the  same  plane. 


LUNAR  TELLURIAN  MANUAL.  13 

36.  The  Equinoctial  Points  or  Equinoxes  are 

the  points  where  the  Ecliptic  crosses  the  Equinoctial. 

The  point  which  the  sun  passes  in  March  is  called  the 
Vernal  Equinox,  and  that  which  he  passes  in  September 
the  Autumnal  Equinox. 

37.  The  Solstitial  Points  or  Solstices  are  the 

two  points  where  the  sun  is  farthest  from  the  Equinoctial. 

The  point  north  of  the  Equinoctial  is  called  the  Sum- 
mer Solstice^  and  the  one  south  the  Winter  Solstice. 

38.  The  Declination  of  a  heavenly  body  is  its  dis- 
tance north  or  south  from  the  Equinoctial. 

Declination  corresponds  to  terrestrial  latitude. 

39.  Perihelion   is   the   point  in   the  earth's   orbit 
nearest  to  the  sun. 

40.  Aphelion  is  the  point  in  the  earth's  orbit  far- 
thest from  the  sun. 

41.  Refraction  in  Astronomy  is  the  change  of  di- 
rection which  the  rays  of  light  undergo  in  passing  through 
the  atmosphere. 

9 

This  may  be  illustrated  to  a  class  by  placing  on  the 
blackboard  a  diagram  ;  thus, 


LUNAR  TELLURIAN  MANUAL. 


F  E  E  F 

Let  S  represent  the  sun,  D  the  earth,  and  F   and  E 

two  strata  of  the    atmosphere   of  which  E  is   the  more 

dense. 

Ask  the  pupil  to  observe, 

(a)  That  if  a  ray  of  light  from  6"  enter  the  stratum  F 
at  3^  it  will  be  bent  toward  the  perpendicular  3b,  and 
enter  the  stratum  E  at  2.  The  stratum  E  being  more 
dense  than  the  stratum  F,  it  is  again  bent  toward  the 
perpendicular  2  &9  and  strikes  the  surface  of  the  earth  at  1. 

(3)  That  the  atmosphere  is  not  made  up,  as  represented 
in  the  diagram,  of  separate  strata  of  different  densities, 
but  becomes  gradually  more  dense  the  nearer  it  is  to  the 
surface  of  the  earth.  Hence,  the  rays  of  light  in  passing 
through  the  atmosphere  curve  gradually  toward  a  per- 
pendicular to  the  surface  of  the  earth  from  the  point 
where  they  enter  the  atmosphere. 

(c)  That  there  Js  no  refraction  when  a  ray  of  light 
strikes  the  atmosphere  perpendicularly,  as  shown  by  the 
line  lz,  and  that  the  more  obliquely  a  ray  enters,  the 
greater  the  refraction,  as  shown  by  the  line  1  3  S.  Hencei 


LUNAR  TELLURIAN  MANUAL.  15 

light  coming  from  any  heavenly  body  in  our  zenith,  un- 
dergoes no  refraction,  and  as  a  body  moves  from  the 
zenith  to  the  horizon,  the  refraction  increases. 

(d)  That  since  all  objects  are  seen  in  the  direction  in 
which  the  light  from  them  falls  upon  the  retina  of  the 
eye,  the  sun  S  in  the  diagram  is  seen  by  an  observer  at 
1  in  the  direction  of  SI.  In  consequence  of  this  effect 
of  refraction  no  heavenly  body,  unless  in  the  zenith,  is 
seen  in  its  real  position. 

In  the  case  of  the  sun  and  moon,  the  amount  of  refrac- 
tion at  the  horizon  is  a  little  greater  than  their  apparent 
diameters.  Hence,  in  rising  or  setting,  they  appear 
above  the  horizon  when  they  are  actually  below  it. 

42.  The  Radiation  of  heat  with  reference  to  the 
earth  is  the  emission  and  diffusion  of  heat  from  its  surface 
into  the  atmosphere. 

Ask  the  pupil  to  observe, 

(a)  That  during  the  day  the  surface  of  the  earth  is 
heated  by  the  rays  of  the  sun. 

(3)  That  when  the  sun  sets  the  earth  radiates  its  heat 
into  the  atmosphere  ;  hence,  the  change  in  the  tempera- 
ture before  the  sun  rises. 

In  the  summer  season  the  earth's  surface  absorbs  or 
takes  in  more  heat  from  the  sun  during  the  long  day  than 
it  radiates  or  gives  out  during  the  short  night,  the  tem- 
perature must  for  this  reason  rise.  When  the  sun  leaves 
us  and  goes  south  our  days  shorten  and  nights  lengthen, 
during  which  absorption  diminishes,  radiation  increases, 
and  the  temperature  is  correspondingly  lowered. 

The  blacksmith  puts  the  horseshoe  into  the  forge  that 


16  LUNAR  TELLURIAN  MANUAL. 

it  may  absorb  heat  until  it  gets  soft,  so  that  he  can  easily 
shape  it  upon  the  anvil  ;  while  working  with  it  the  shoe 
radiates  heat,  getting  thereby  more  and  more  difficult  to 
work.  It  must  soon  be  replaced  in  the  forge  again  to 
absorb  the  required  quantity  of  heat  to  be  easily  arid 
economically  wrought  ;  when  the  smith  is  through  with 
the  shoe  he  drops  it  into  his  tub  of  water  that  it  may 
quickly  radiate  the  heat  and  be  ready  to  nail  to  the 
horse's  hoof. 

Distribution  of  Light  and  Heat. 

To  Illustrate  the  difference  between  the  Sun's  Ver- 
tical and  Oblique  Rays. 

Take  two  pieces  of  cardboard  about  a  foot  square.  In 
the  center  of  one  of  them  cut  a  round  hole  about  one 
inch  in  diameter  ;  hold  this  one  up  to  the  sun  at  a  right 
angle  to  the  rays,  so  that  the  light  will  pass  through  the 
opening  ;  place  the  other  piece  about  a  foot  behind  the 
first  and  parallel  to  it  ;  ask  the  pupils  to  observe  that  the 
sunlight  passing  through  the  inch  opening  falls  upon  the 
second  piece  vertical  to  it,  and  covers  a  like  surface  of  one 
inch.  This  illustrates  how  the  sunlight,  falling  verti- 
cally upon  the  earth,  covers  a  surface  equal  to  the  volume 
of  such  light. 

Change  the  position  of  the  back  piece  of  cardboard 
slowly,  so  that  it  will  not  be  parallel  to  the  first,  and  ask 
the  pupils  to  observe  that  while  no  more  sunlight  passes 
through  the  opening  in  the  first  cardboard  than  in  the 
other  illustration,  yet  that  amount  is  spread  over  a  greater 
surface  on  the  second  piece,  owing  entirely  to  the  fact 
that  it  now  falls  obliquely  ;  whereas,  in  the  first  instance, 
it  fell  vertical  to  the  surface  of  the  cardboard.  This  illus- 


LUNAR  TELLURIAN  MANUAL.  17 

trates  how  the  sunlight,  falling  obliquely  upon  the  earth's 
surface,  covers  a  space  greater  in  area  than  the  volume 
of  the  light.  Observe  also,  that  the  greater  the  obliquity  ? 
the  greater  the  space  covered. 

Remove  the  second  piece  of  cardboard,  and  put  the 
globe  in  its  place  in  such  a  manner  that  the  sunlight  ad- 
mitted through  the  first  cardboard  shall  fall  vertical  to 
the  surface  upon  the  equator.  Observe  that  the  area  of 
light  on  the  surface  of  the  globe  is  about  equal  to  the  area 
of  the  hole  admitting  the  light.  Raise  the  cardboard  so 
that  the  sunlight  will  fall  upon  the  40th  parallel  of  north 
latitude,  and  observe  that  while  no  more  sunlight  is  ad- 
mitted, it  covers  a  much  greater  area,  and  must  be  less 
intense  there  than  on  the  equator  where  the  sun  was 
vertical.  In  the  same  manner  place  the  sunlight  on  the 
60th  parallel,  and  observe  the  greater  obliquity  and  the 
greater  area  covered.  Call  special  attention  to  the  fact 
that  the  curvature  of  the  globe  is  the  only  cause  of  the 
rays  in  the  higher  latitude  being  more  oblique  than  they 
are  in  the  lower  latitudes. 

Observe,  that  what  is  true  of  a  small  globe  and  a  por- 
tion of  sunlight,  is  true  of  our  earth  as  a  sphere,  and 
the  greater  volume  of  sunlight,* 

Thus  we  find — 

i.  That  the  nearer  the  vertical  sun,  the  more  intense 
the  light  and  heat  ;  and  the  farther  from  the  vertical 
sun,  the  less  intense  the  light  and  heat. 

The  cause  of  the  heat  of  summer  and  cold  of  winter 
is  not  more  due  to  the  angle  at  which  the  rays  of  sun- 
light strike  us,  than  to  the  relative  lengths  of  day  and 
night  at  these  seasons.  In  midsummer  we  are  about  15 


i8  LUNAR  TELLURIAN  MANUAL. 

hours  in  sunlight,  wherein  we  are  warming,  and  about 
9  hours  are  turned  away  in  darkness  to  cool,  while  in 
midwinter  we  have  about  9  hours  of  sunlight  and  15 
hours  of  darkness.  As  we  depend  upon  sunlight  for 
heat,  it  follows  that  the  temperature  must  rise  in  summer 
and  fall  in  winter,  owing  to  the  longer  and  shorter  periods 
of  sunshine  at  these  respective  seasons. 

2.  That  only  one-half  of  the  earth's  surface  can  at 
any  time,  be  exposed  to  the  sun's  light  and  heat.  This 
half  is  called  the  Illuminated  Hemisphere. 

Rotate  the  globe  on  its  axis  from  west  to  east  10  de- 
grees, and  ask  the  pupils  to  observe,  in  case  the  earth 
moves  in  like  manner  : 

(a)  That  a  distribution   of  light   and   heat   will   have 
taken  place. 

(b)  That  the  vertical  rays  of  the  sun   will   have  been 
carried  westward  10   degrees  upon  the  earth's  surface, 
owing  to  this  rotation  to  the  east ;  or,  the  sun's  vertical 
ray  will  have  been  distributed  east  and  west  10  degrees. 

(c)  That  the  boundary  of  sun's  light  and  heat  will  have 
been  carried  westward  from  90  degrees  west  longitude 
to  100  degrees,  and  that  all  places  situated  between  these 

*NOTL. — If  convenient,  place  a  convex  lens  over  the  aperture  in 
the  cardboard  ;  place  the  second  board  behind,  as  directed  in  the 
first  instance,  and  at  such  a  distance  as  necessary  to  make  the 
converging  rays  cover  the  least  possible  surface  ;  hold  the  sunlight 
upon  the  same  point  for  a  few  moments  ;  and  if  the  lens  is  a  good 
one,  combustion  will  ensue  at  the  point  of  contact,  thus  illustrat- 
ing the  intense  heat  produced  by  reducing  the  space  covered  by  a 
given  portion  of  sunlight.  The  intensity  of  solar  heat  is  inversely 
proportional  to  the  space  covered  by  a  given  volume. 


LUNAR  TELLURIAN  MANUAL.  19 

meridians  will  have  been  by  this  distribution  brought 
into  the  illuminated  hemisphere,  while  those  places  situ- 
ated between  the  90th  and  80th  meridians  east  longitude 
will  have  been  carried  out  of  it. 

(d)  That  the  Day  and  Night  Circle  is  parallel  with 
the  meridians  as  they  pass  under  it. 

Rotate  the  globe  once  upon  its  axis  from  west  to  east, 
and  ask  the  pupils  to  observe  : 

(a)  That  by  reason  of  this  rotation  the  sun  has  crossed 
every  meridian  and  returned  to  the  place  of  starting. 

(b)  That  every  meridian  has  passed  through  the  illu- 
minated and  the  dark    hemispheres.     Hence,   one  com- 
plete distribution    of  light  and    heat   east  and   ivest  has 
taken  place,  being  produced  by  the  rotation  of  the  earth 
upon  its  axis.     As  the  earth  turns  once  upon  its  axis  daily, 
there  must  occur  a  daily  distribution  oj~  light  and  Tieat 
east  and  west  upon  the  eart/i's  surface. 

(c)  That  when  the  sun  is  vertical  to  the  equator,  as  on 
March  20th  and  September  23rd,  the  light  and   heat  of 
the  sun   is  equally  distributed   in  the  north   and    south 
hemispheres. 

To  Illustrate  the  Distribution  of  Light  and  Heat 
on  March  2Oth. 

To  produce  a  distribution  of  the  sun's  light  and  heat 
upon  the  earth's  surface,  the  earth  or  sun  must  change 
their  position  in  respect  to  the  other.  This  necessitates 
a  movement,  and  without  a  movement  no  distribution 
can  take  place. 

It  is  very  necessary  that  the  pupils  get  a  clear  concep- 
tion of  this  subject  and  master  it,  as  upon  the  distribution 


20  LUNAR  TELLURIAN  MANUAL. 

of  light  and  heat  depend  the  succession  of  day  and  night, 
the  twilights,  change  of  seasons,  and,  in  fact,  our  very 
existence. 

Bring  the  calendar  index  to  the  20th  of  March  ;  rotate 
the  globe  upon  its  axis  until  the  sun  is  vertical  to  the 
prime  meridian,  and  ask  the  pupils  to  observe  : 

(a)  That  the  sun  is  vertical  to  the  equator. 

(b)  That  the  sun's  light  and   heat  extends  north  and 
south  from  pole  to  pole,  as  shown  by  the  Day  and  Night 
Circle  B. 

(c)  That   the  sun's   light  and   heat  extends  east  and 
'west  of  the  prime  meridian  90  degrees,  as  shown  by  the 
Day  and  Night  Circle  B. 

To  Illustrate  the   Distribution  of  Light  and  Heat 
on  the  21st  of  June. 

Bring  the  calendar  index  to  the  21st  of  June,  and  ask 
the  pupils  to  observe  : 

(a)  That  the  sun  is   vertical  to  the  Tropic  of  Cancer, 
23  yz  degrees  north  of  the  equator. 

(b)  That  the  Illuminated    Hemisphere  now    extends 
23 y^  degrees  beyond  the  north  pole,  and  that  it  fails  to 
reach  the  south  pole  by  the  same  number  of  degrees. 

(c]  That  the  place  upon  the  earth's  surface  where  the 
vertical  ray  falls,  is  the  center  of  the  Illuminated  Hemi- 
sphere, and  that  any  change  in  position  of  this  point  pro- 
duces a  like  change  in  the  Illuminated,  and  an   opposite 
change  in  the  Dark  Hemispheres. 

(d]  That  on  June  21st  the  light  and  heat  of  the  sun  is 
unequally  distributed  in  the  north  and  south  hemispheres  ; 


LUNAR  TELLURIAN  MANUAL.  21 

that  the  Illuminated  Hemisphere  predominates  north  of 
the  equator,  and  the  Dark  Hemisphere  predominates 
south  of  it. 

Rotate  the  globe  upon  its  axis,  and  ask  the  pupils  to 
observe  : 

(a)  That  the  vertical  sun  traces  the  Tropic  of  Cancer. 

(3)  That  as  the  earth  rotates  upon  its  axis,  in  this  man- 
ner, all  places  within  the  Arctic  circle  will  remain  in 
sunlight,  while  corresponding  places  within  the  Antarctic 
will  remain  without  sunlight. 

(c)  That  from  the  20th  of  March  to  the  21st  of  June, 
the  vertical  sun  has  been  carried  north  23*^  degrees,  or 
that  a  north  and  south  distribution  to  the  extent  of  23 ^ 
degrees  has  taken  place. 

To  Illustrate  the  Distribution  of  Light  and  Heat 
on  the  23d  of  September. 

Bring  the  calendar  index  to  the  23d  of  September  ; 
this  illustrates  the  relationship  that  exists  between  the 
earth  and  sun  on  that  day.  Ask  the  pupils  to  observe  : 

(a)  That  the  vertical  sun  has,   from    the  21st  of  June 
to  the  23d  of  September,  been    carried   south    from  the 
Tropic  of  Cancer  to   the  equator  ;  and  that  the  Illumin- 
ated Hemisphere  has  been  correspondingly  changed,  so 
that  on  September  23d,  the  sun's  light  and  heat  is  again 
equally  distributed  in  the  north  and  south  hemispheresi 
and  extending  from  pole  to  pole,  as  on  March  20th. 

(b)  That  whatever  distribution  was  shown,  or  what- 
ever observations   could   be    made  on  March  20th,  are 
again  reproduced  on  September  23d. 


22  LUNAR  TELLURIAN  MANUAL. 

To  Illustrate  the  Distribution     of  Light  and  Heat 
on  December  22d. 

Bring  the  calendar  index  to  the  22d  of  December,  and 
ask  the  pupils  to  observe  : 

(a)  That  the  sun  is  vertical  23^  degrees  south  of  the 
equator. 

(b)  That  the    Illuminated    Hemisphere  now   extends 

23  y2  degrees  beyond  the   south   pole,  and  that  it  fails  to 
reach  the  north  pole  by  the  same  number  of  degrees. 

(c)  That,  on  December   22d,  the  light  and  heat  of  the 
sun  is  again  unequally  distributed  in  the  north  and  south 
hemispheres,  and  that  the  Illuminated  Hemisphere  pre- 
dominates  south  of  the   equator,  and   the   Dark   Hemi- 
sphere predominates  north  of  it. 

Rotate  the  globe  upon  its  axis,  and  ask  the  pupils  to 
observe  : 

(a)  That  the  vertical  sun  traces  the  Tropic  of  Capri- 
corn. 

(b)  That  as  the  earth  rotates  upon   its    axis   in   this 
manner,  all  places  within  the  Antarctic  circle  remain  in 
sunlight,  while  corresponding  places  within  the  Arctic 
circle  will  remain  without  sunlight. 

(c)  That  from  the  23d  of  September  to  the  22d  of 
December  the  vertical  sun  has  been  carried  south  23^ 
degrees,  or  that  a  north  and  south  distribution  has  taken 
place. 

Bring  the  calendar  index  slowly  to  starting  point 
(March  20th,)  and  observe  :  That  the  vertical  sun  is 
carried  from  the  Tropic  of  Capricorn  to  the  equator,  the 
place  of  beginning;  and  that  a  north  and  south  distribu- 


LUNAR  TELLURIAN  MANUAL.  23 

tion  of  the  sun's  light  and  heat  has  taken  place  from  the 
equator  to  both  tropics  and  return,  and  that  the  time 
necessary  to  do  this  is  one  year  ;  and,  as  the  vertical  ray 
is  distributed,  so  must  all  other  rays  that  touch  the 
earths  surface  be  affected. 

Thus  we  see  that  there  is  a  double  distribution  :  east 
and  west  daily,  and  north  and  south  annually. 

The  Causes  of  the  Existing  Distribution  of  Light 
and  Seat. 

1.  The  daily  distribution  east  and  west  is  caused  by 
the  daily  rotation  of  the  earth  on  its  axis. 

2.  The  annual  distribution  north  and  south  is  caused : 

(a)  By  the  revolution  of  the  earth  in  its  orbit  around 
the  sun.  If  the  earth  remained  fixed  in  its  orbit,  and 
revolved  upon  its  axis,  but  one  distribution  could  take 
place — the  daily. 

(3)  By  the  inclination  of  the  earth's  axis.  Notice  that 
on  the  20th  of  March  the  axis  is  inclined  23^  degrees, 
but  that  the  inclination  is  neither  to  nor  from  the  sun, 
and  that  the  sun  is  then  vertical  to  the  equator.  Notice 
that  on  the  21st  of  June  the  north  pole  is  inclined  to  the 
sun  the  full  inclination  of  23^  degrees,  and  for  this 
reason  the  sun  is  vertical  the  same  number  of  degrees 
north  of  the  equator.  On  December  22d,  the  north  pole 
is  inclined  from  the  sun  the  full  inclination,  this  bring- 
ing Capricorn  under  the  sun.  Erect  the  axis  by  sup- 
porting the  globe  on  the  other  socket,  call  the  pupil's 
attention  to  the  fact  that  the  equator  and  the  ecliptic 
now  lie  in  the  same  plane.  Revolve  the  earth  around 
the  sun  and  observe  that  the  vertical  ray  falls  constantly 


24  LUNAR  TELLURIAN  MANUAL. 

upon   the  equator  ;    without   an    inclination    no    annual 
distribution  of  light  and  heat  could  take  place. 

(c)  By  the  parallelism  of  the  eartJi's  axis.  The  axis 
is  said  to  be  parallel,  because  it  points  continually  to  the 
same  part  of  the  heavens  I  thus,  the  north  pole  points 
constantly  towards  the  North  Star,  while  the  earth  re- 
volves around  the  sun.  Revolve  the  globe  around  the 
arc  S  and  observe  that  the  axis  points  constantly  in  the 
same  direction.  This  is  true  of  the  earth  and  all  the 
planets  as  they  revolve  in  their  several  orbits.  This  is 
termed  the  parallelism  of  the  axis. 

Equal  Days  and  Nights. 

1.  Bring  the  calendar  index  to  the  20th  of  March, 
and  ask  the  pupils  to  observe  : 

(a)  That  the  Day  and  Night  Circle  B  divides  the 
earth  into  two  divisions — day  and  Night  :  that  all  places 
on  the  side  of  this  circle  next  to  the  sun  have  day,  while 
those  places  on  the  opposite  side  have  night. 

(6)  That  at  this  season  of  the  year  the  sun  is  vertical 
to  the  equator,  and  the  Day  and  Night  Circle  is  parallel 
to  opposite  meridians. 

*(c)  That  in  this  position  the  Day  and  Night  Circle 
divides  every  parallel  of  latitude,  from  pole  to  pole, 
into  tivo  equal  parts. 

Rotate  the  globe  slowly  upon  its  axis,  and  ask  the 
pupils  to  observe  : 

(a)  That  all  places  upon  a  given  meridian  enter  the 
sunlight  at  the  same  moment. 

(&)  That  one-half  a  rotation  on  the  axis  carries  these 


TELLURIAN  MANUAL.  25 


places  through  the  Illuminated  Hemisphere,  where  they 
pass  beyond  the  Day  and  Night  Circle,  when  the  day 
ends  and  night  begins. 

(c)  That  one-half  a  rotation  carries  these  places  from 
sunset  to  sunrise. 

Thus  we  see  that  on  March  20th,  the  days  and  nights 
must  be  equal  all  over  the  earth's  surface. 

Bring  the  calendar  index  to  the  23d  of  September,  and 
ask  the  pupils  to  notice  that  the  same  condition  that  ex- 
isted on  March  20th,  again  exists,  with  the  same  result  — 
equal  days  and  nights. 

Unequal  Days  and  Nights. 

Bring  the  calendar  index  to  the  21st  of  June,  and  ask 
the  pupils  to  observe  : 

(a)  That  the  sun  is  vertical  23  ^  degrees  north  of  the 
equator,    and   that   the   sunlight    extends    23^    degrees 
beyond  the  north  pole,  and   fails  to  reach  the  south  pole 
by  the  same  number  of  degrees. 

(b)  That  the  Day  and   Night  Circle  no  longer  divides 
the  parallels  of  latitude  into  equal   parts,  but  into  two 
unequal  parts  ;  and  that  north  of  the  equator  the  greater 
part  of  every  parallel  is  in  the  sunlight,  and  the  lesser 
part  in  darkness  ;  while  south  of  the  equator  the  lesser 
part  is  in  sunlight,  and  the  greater  part  in  darkness. 

(c)  That  the  entire  parallels  within  23  yz   degrees  of 
the  north   pole    are   now  in  constant  day,  while  those 
within  the  same  distance  of  the  south  pole  are  in  con- 
tinual night. 

Rotate  the  globe  on  its  axis,  and  ask  the  pupils  to 
observe  : 


26  LUNAR  TELLURIAN  MANUAL. 

• 

(a)  That  no  sunlight  or  day  reaches  that  portion  of 
the  earth's  surface  within  the  Antarctic  circle,  although 
the  earth  may  revolve  upon  its  axis. 

(£)  That  the  entire  area  of  the  earth's  surface  within 
the  Arctic  circle,  is  not  carried  out  of  the  sunlight  by  the 
rotation  of  the  earth  upon  its  axis. 

(c)  That  the  Day  and  Night  Circle  cuts  the  equator  at 
opposite  points,  and  that  there  the   days  and  nights  are 
equal. 

(d)  That,  as  you  proceed    north  from   the  equator  to 
the  Arctic  circle,  the  days  increase  in  length  gradually 
from  12  hours  at  the  equator,  to  24  hours  within  the  Arc- 
tic Circle. 

(e)  That,  as  you  proceed  south  from  the  equator  to  the 
Antarctic  circle,  the  days  decrease  in  length  gradually, 
from  12  hours  at  the  equator,  to  0  hours  within  the  Ant- 
arctic Circle. 

Bring  the  calendar  index  to  the  22cl  of  December,  and 
ask  the  pupils  to  observe  :  that  what  was  true  of  the 
northern  in  June,  is  now  true  of  the  southern  hemi- 
sphere in  December.  Thus  it  is  evident — 

1.  That  when  the  sun  is  upon  the  equator,  the  days 
and  nights  are  everywhere  equal. 

2.  That  when  the  vertical  sun  is  one  or  more  degrees 
north  or  south  of  the  equator,  continual   day  must  exist 
around  the  pole  nearer  the  sun,  and  continual  night  must 
exist  around  the  pole  farther  from  the  sun  ;  the  extent 
of  this  area  of  continual  day  and  night  depending  upon 
the  distance  of  the  vertical  sun   north  or  South  of  the 
equator. 


LUNAR  TELLURIAN  MANUAL.  27 

3.  That  the  days  and  nights  at  the  equator  must  al- 
ways be  equal. 

4.  That  as  you  depart  from  the  equator,  the  variation 
in  the  length  of  day  and  night  increases,  and  as  you  ap- 
proach the  equator  the  variation  becomes  less  :  the  max- 
imum variation  being  in  the  polar,  and  the  minimum  in 
the  equatorial  regions. 

5.  That  the  length  of  any  day   upon  any  parallel  of 
north  latitude,  is  equal  to  the  night  following  on  the  cor- 
responding parallel  of  south  latitude. 

NOTE. — In  this  work  we  regard  day  as  the  time  when  the  sun 
is  present,  and  night  as  the  time  when  he  '^absent.  Night  does 
not  necessarily  mean  darkness.  Night  begins  at  sunset  and  ends 
at  sunrise. 

The  Sun's  Apparent  Path. 

Bring  the  calendar*  index  to  the  21st  of  June,  rotate 
the  globe  on  its  axis  until  the  Ecliptic  marked  upon  the 
globe  is  brought  under  the  vertical  Sun.  Move  very 
slowly  the  calendar  index  through  the  succeeding  months 
until  it  again  comes  to  the  21st  of  June,  and  ask  the 
pupils  to  notice  that  the  vertical  sun  traces  the  ecliptic 
and  if  the  earth  had  no  daily  rotation  on  its  axis,  that  the 
ecliptic  would  mark  the  true  path  of  the  Sun  upon  the 
earth. 

Rotate  the  earth  upon  its  axis  and  ask  the  pupils-  to 
observe  that  the  Sun  traces  the  Tropic  of  Cancer,  and 
that  if  the  sun  should  leave  behind  it  a  thread  of  light> 
that  thread  would  lie  upon  the  tropic.  Move  the  calen- 
dar index  to  the  22d  of  June,  and  rotate  the  globe  upon 
its  axis,  and  notice  that  the  sun  traces  a  line  parallel  to 
the  Tropic  of  Cancer,  but  about  *£  of  a  degree  south  of 
it.  In  the  same  manner  proceed  with  several  days  in 


28  LUNAR  TELLURIAN  MANUAL. 

succession  and  observe  that  by  reason  of  the  rotation  of 
the  earth  upon  its  axis  and  the  movement  forward  of 
the  earth  in  its  orbit  at  the  same  time,  the  path  of  the 
vertical  sun  will  be  a  continuous  line  running  from  east 
to  west,  and  winding  south  from  Cancer  to  Capricorn, 
and  returning  during  the  year,  much  as  a  thread  is  wound 
upon  a  spool. 

Change  of  Seasons. 

To  produce  what  is  called  a  change  of  season  at  any 
place,  more  solar  heat  must  fall  upon  that  place  during 
one  part  of  the  year  than  at  another.  Within  the  tropics 
the  amount  of  heat  received  from  the  sun  is  nearly  uni- 
form throughout  the  year,  so  that  very  little  change  of 
season  takes  place  ;  the  greatest  changes  occurring  in 
the  higher  latitudes. 

Bring  the  calendar  index  to  the  20th  of  March  and 
ask  the  pupils  to  observe  : 

(a)  That  the  light  and  heat  of  the  sun  are  equally  dis- 
tributed in  the  north  and  south  Hemispheres. 

(6)  That  if  the  earth  remained  fixed  in  its  orbit  and 
was  rotated  upon  its  axis,  there  could  be  no  change  of 
seasons. 

Bring  the  calendar  index  to  the  21st  of  June  and  ask 
the  pupils  to  observe  : 

(a)  That  the  sun  is  now  vertical  to  the  tropic  of  can- 
cer, and  that  the  sun's  light  and  heat  is  unequally  dis- 
tributed in  the  north  and  south  hemispheres,  the  north 
hemisphere  having  the  greater  and  the  south  hemisphere 
the  lesser  amount. 


LUNAR  TELLURIAN  MANUAL.  29 

(b)  That  owing  to  this  inequality 4jie  north  hemisphere 
is  having  its  greatest  amount  of  light  and  heat,  its 
warmest  season  or  Summer,  and  that  the  south  hemi- 
sphere is  having  its  coldest  season  or  Winter. 

Bring  the  calendar  index  to  the  23d  of  September  and 
ask  the  pupils  to  observe  that  the  light  and  heat  is  again 
equally  distributed  north  and  south  of  the  equator  as  in 
March  20th. 

Bring  the  calendar  index  to  the  22d  of  December  and 
ask  the  pupils  to  observe  that  the  sun  is  vertical  to  the 
tropic  of  Capricorn,  the  sun's  light  and  heat  being  again 
uneqally  distributed  in  the  north  and  south  hemispheres, 
the  south  having  the  greater  and  the  north  the  lesser 
amount  ;  and  that  at  this  time  in  the  year  the  south 
hemisphere  is  having  the  warmest  season  or  Summer, 
while  in  the  north  it  is  in  the  coldest  or  Winter  season. 

Bring  the  calendar  index  to  the  20th  of  March,  and 
observe  that  the  sun  is  brought  to  the  equator  going 
north  and  that  as  it  crosses,  Spring  begins  in  the  north 
and  Autumn  or  Fall  begins  in  the  south  hemisphere. 

The  Causes  that  produce    the  Change    of 
Seasons. 

The  change  of  seasons  is  produced  by, 

(a)  The  revolution  of  the  earth  in  its  orbit  around  the 
sun. 

(b)  The  inclination  of  the  earth's  axis  to  the  plane  of 
the  orbit. 

(c)  The  parallelism   or  fixed  position  of  the   earth's 
axis. 


30  LUNAR  TELLURIAN  MANUAL. 

(d)  The  rotation  of  the  earth  upon  its  axis. 

To  illustrate  that  the  rotation  of  the  earth  upon  its 
axis  is  one  of  the  causes  that  produce  the  changes  of  sea- 
sons as  they  now  exist  :  bring  the  calendar  index  to  the 
20th  of  March,  mark  the  point  upon  the  equator  where 
the  sun  is  vertical  at  that  time  ;  now  move  the  calendar 
index  slowly  through  the  succeeding  months  of  the  year 
until  it  is  again  vertical  to  the  same  point.  Call  the 
pupil's  attention  to  the  fact  that  if  the  earth  did  not 
rotate  upon  its  axis  the  sun  would  require  one  year  to 
cross  all  the  meridians  once,  and  that  in  this  case  it 
would  cross  them  from  west  to  east  instead  of  from  east 
to  west;  that  the  sun  would  in  that  event  rise  in  the  ivest 
and  set  in  the  east,  and  our  day  and  year  would  be  of 
the  same  length  ;  and,  that  if  this  were  true,  the  side  of 
the  earth  towards  the  sun  would  be  parched  by  the  ex- 
treme heat,  while  the  opposite  side  would  become  frozen 
and  lifeless.  So,  if  the  earth  did  not  rotate  on  her  axis, 
no  changes  of  seasons  as  they  now  exist  could  take  place, 
nor  in  fact  could  animal  or  vegetable  life  as  now  con- 
stituted endure  the  extremes  of  heat  and  cold  to  which 
they  would  be  subjected. 

Twilights. 

To  show  how  the  sun  after  going  below  the  horizon 
continues  to  give  reflected  light,  and  hence,  produces 
twilight. 

* 

The  molecules  of  which  the  atmosphere  is  composed, 
reflect  the  light  they  receive  from  the  sun,  and  by  the 
light  so  reflected,  objects  .are  seen  in  the  absence  of  direct 
sunlight  The  atmosphere  is  capable  of  thus  reflecting 


LUNAR  TELLURIAN  MANUAL.  31 

light  a  mean  distance  of  18  degrees  of  a  great  circle. 
Call  the  pupils'  attention  to  the  fact  that  the  sun  gives 
direct  light  from  the  point  where  he  is  vertical  to  the 
Day  and  Night  Circle  B,  and  that  the  indirect  or  reflected 
light  extends  to  thfc  circle  C,  and  that  file  space  between 
these  circles  is  called  the  Twilight  Belt.  Hence  the 
earth's  surface  as  regards  light  is  divided  into  three  sec- 
tions :  1.  A  hemisphere  of  direct  light.  2.  A  belt  18 
degrees  wide  of  reflected  light  or  twilight.  3.  The  re- 
maining portion  without  light. 

To  Illustrate  the   Twilight  on  the  20th  of  March. 

Bring  the  calendar  index  to  the  20th  of  March.  Call 
the  pupil's  attention  to  the  fact  that  there  are  two  twi- 
lights, Evening  and  Morning  ;  that  the  evening  twilight 
deepens  into  darkness,  while  the  morning  twilight  bright- 
ens into  sunshine.  Rotate  the  globe  upon  its  axis  and 
ask  the  pupils  to  observe  :  that  places  upon  the  earth's 
surface  must  cross  the  twilight  belt  twice  in  every  24 
hours.  Rotate  the  globe  slowly  upon  its  axis  and  ask 
the  pupils  to  observe  :  that  all  places  upon  the  same 
meridian  from  pole  to  pole  pass  into  evening  twilight  at 
the  same  instant,  but  that  those  places  located  near  the 
equator  pass  out  of  twilight  first,  and  that  the  higher  the 
latitude  the  longer  the  twilight  continues.  This  varia- 
tion is  due  : 

1st.    To  the  fact  that  at  the  equator  the  earth  rotates 
faster  than  it  does  near   the  poles,  for  the  same  reason 
that  the  outer  part  of  a  wagon  wheel  turns  faster  when 
the  wagon  is  in  motion,  than  the  hub. 

2d.  This  variation  is  partially  due  to  the  fact  that 
places  near  the  equator  are  carried  across  the  twilight 


32  LUNAR  TELLURIAN  MANUAL. 

belt  in  a  straight  line,  and  at  right  angles  to  it  :  while 
near  the  poles  places  enter  the  twilight  at  right  angles 
with  the  first  circle  and  cross  the  belt  not  in  a  direct  line, 
but  travel  on  an  arc  of  a  circle  passing  obliquely  across 
the  second  circle.  • 

From  this  we  see  that  places  in  the  higher  latitudes 
must  travel  farther  to  cross  the  twilight  belt,  and  at  the 
same  time,  much  slower  than  those  places  situated  near 
the  equator. 

Locate  upon  the  map  of  the  globe  the  place  where 
you  are  situated,  rotate  the  globe  upon  its  axis  and  ask 
the  pupils  to  note  carefully  the  manner  this  place  is 
carried  across  the  twilight  belt.  This  illustrates  the  twi- 
lights on  the  20th  of  March,  for  that  place. 

To  Illustrate  the  Twilights  on  the  21st  of  June. 

Bring  the  calendar  index  to  the  21st  of  June  and  ask 
the  pupils  to  observe  : 

(a)  That  the  twilight  belt  no  longer  conforms  to  the 
meridians,  and  that  no  two  places  upon  the  same  meri- 
dian enter  the  evening  or  emerge  from  the  morning 
twilight  at  the  same  moment. 

(&)  Those  places  that  in  March  cross  the  twilight  belt 
at  right  angles  to  it,  now  cross  it  obliquely,  so  that  the 
twilights  for  these  places  must  be  longer  in  June  than  in 
March. 

(c)  That  the  obliquity  is  least  at  the  equator,  and  in- 
creasing as  the  latitude  increases. 

Locate  upon  the  map  of  the  globe  the  place  where 
you  are  located,  rotate  the  globe  upon  its  axis  and  ask 


TM£ 

UNIVERSITY 

OF 

SSL 

LUNAR  TELLURIAN  MANUAL.  33 

the  pupils  to  observe  that  this  place  is  carried  across  the 
twilight  belt  more  obliquely  than  in  March,  and  that  the 
twilight  must  be  of  longer  duration. 

To  Illustrate  the  Twilight  on  the  23d  of  September. 

Bring  the  calendar  index  to  the  23d  of  September,  ex- 
amine the  twilight  in  the  same  manner  as  upon  the  20th 
of  March,  and  ask  the  pupils  to  notice  that  all  the  facts 
are  the  same  as  were  observed  at  that  date. 

To  Illustrate  the  twilight  on  the  22d  of  December. 

Bring  the  calendar  index  to  the  22d  of  December,  and 
ask  the  pupils  to  notice  that  places  upon  the  earth's  sur- 
face are  carried  across  the  twilight  belt  obiquely  substan- 
tially as  in  June. 

Compare  the  twilights  of  any  place*  at  different  dates 
by  use  of  the  globe,  taking  the  21st  of  June  as  the  basis 
of  comparison,  and  repeat  the  comparison  until  the  pu- 
pils see  clearly, 

(a)  That  on  the  21st  of  June  the  given  place  crosses 
the   Twilight  Belt  more  obliquely  than  on  either  of  the 
other  dates,  and  hence  the  longest  twilight. 

(b)  That  on  the  20th  of  March  and  23d  of  September, 
the  path  of  the  given  place  across  the  Twilight  Belt  is 
the  same,  and  less  oblique  than  at  either  of  the  other 
dates,  and  hence  the  shortest  twilight. 

(c)  That   on   the   22d  of  December  the   given  place 
crosses  the  Twilight  Belt  less  obliquely  than  on  the  21st 

*The  author  would  suggest  that  the  place  selected  be  in  north  latitude  40 
to  50  degrees. 


34  LUNAR  TELLURIAN  MANUAL. 

of  June,  and  more  obliquely  than  on  the  20th  of.  March 
and  23d  of  September.  Hence,  a  mean  twilight  between 
the  other  two. 

3d.  Now  ask  the  pupils  to  notice  that  on  the  22d  of 
December  the  sun  is  vertical  to  south  latitude  23^,  and 
on  the  21st  of  June,  north  latitude  23^.  Consequently 
the  sun  sustains  the  same  relation  in  every  particular  to 
the  Southern  Hemisphere  at  the  former  date,  that  it  does 
at  the  latter  date  to  the  Northern.  Hence,  all  the  facts 
observed  regarding  the  twilight  on  the  21st  of  June  in 
northern  latitudes  apply  on  the  22d  of  December  to  cor- 
responding southern  latitudes.  Hence,  all  the  facts  ob- 
served on  the  22d  of  December  in  northern  latitudes  may 
be  found  on  the  21st  of  June  in  the  southern  latitudes. 

Sun's  Declination. 

The  Sun's ,  Declination  is  his  distance  north  or  south 
of  the  equator  (as  indicated  by  the  vertical  ray).  When 
the  sun  is  north  of  the  equator  he  is  said  to  have  a  north- 
ern declination  ;  when  south  of  the  equator  he  is  said  to 
have  a  southern  declination. 

The  greatest  northern  declination  (23 1^  degrees)  oc- 
curs on  the  21st  of  June,  and  the  greatest  southern  de- 
clination (23 yz  degrees)  occurs  December  22d.  At  the 
time  of  the  equinoxes  (March  20  and  September  23d), 
the  sun  has  no  declination. 

To  Find  the  Sun's  Declination  for  any  Day. 

Bring  the  calendar  index  to  the  given  day,  rotate  the 
globe  upon  its  axis  until  the  meridian  having  the  degrees 
upon  it  is  brought  under  the  pointer  L.  Extend  the 


LUNAR  TELLURIAN  MANUAL.  35 

pointer  L  to  the  globe.     The  degree  of  latitude  under 
the  pointer  is  the  required  Declination. 

To  Find  the  Longitude  of  any  Place, 

Rotate  the  globe  upon  its  axis  until  the  given  place  is 
under  the  pointer  H,  the  degree  on  the  equator  at  the 
end  of  the  pointer  H  is  the  longitude  required.  The 
longitude  is  east  or  west  according  as  the  place  is  east  or 
west  of  the  Prime  Meridian. 

EXAMPLES. 

1.  What  is  the  longitude  of  New  York  ? 

2.  What  is  the  longitude  of  Calcutta  ? 

3.  What  is  the  longitude  of  Quito  ? 

4.  What  is  the  longitude  of  St.  Petersburg  ? 

5.  What  is  the  longitude  of  Honolulu  ? 

To  Find  the  Latitude  of  any  Place. 

Rotate  the  globe  upon  its  axis  until  the  given  place  is 
brought  under  the  pointer  H,  above  the  place  on  the 
pointer  read  the  degree  of  latitude  required  ;  or,  bring 
the  given  place  under  the  edge  of  circle  B,  mark  the 
circle  directly  over  the  given  place,  rotate  the  globe  until 
the  meridian  having  the  degrees  marked  upon  it  is  brought 
under  the  circle.  Under  the  point  marked,  read  upon 
the  meridian  the  degree  of  latitude  required.  If  the 
place  is  north  of  the  equator  it  is  north  latitude,  if  south 
of  it,  south  latitude. 

EXAMPLES. 

1.  What  is  the  latitude  of  New  York  ? 

;2.  What  is  the  latitude  of  Calcutta  ? 

3.  What  is  the  latitude  of  Quito  ? 

4.  What  is  the  latitude  of  St.  Petersburg  ? 

5.  What  is  the  latitude  of  Honolulu  ? 

6.  What  is  the  latitude  of  Santiago  ? 


LUNAR     TELLURIAN    MANUAL. 


CUT  No.  2. 


Remove  the  day  and  night  circle,  as  in  the  above  cut. 
As  now  seen,  the  Lunar  Tellurian  should  be  used  to 
explain  the  phases  of  the  moon,  eclipses,  equation  of 
time,  precession  of  equinoxes,  etc. 

36 


LUNAR  TELLURIAN  MANUAL.  37 

Longitude  and  Time. 

Longitude  is  distance,  measured  however  in  degrees, 
minutes  and  seconds,  east  or  west  of  a  given  meridian 
called  the  Prime  Meridian.  Observe  that  the  degrees 
are  marked  upon  the  globe  at  the  equator,  east  and  west 
from  the  meridian  of  Greenwich — the  Prime  Meridian. 

On  page  (9)  we  learned  that  every  circle  is  divided 
into  360  equal  parts  called  degrees,  every  degree  is  sub- 
divided into  60  equal  parts  called  minutes,  and  every 
minute  is  subdivided  into  60  equal  parts  called  seconds. 
The  earth  in  its  relation  to  the  sun  turns  once  on  its 
axis  (360  degrees)  every  24  hours,  and  must  turn  as  many 
degrees  every  hour  as  24  is  contained  times  in  360  or  15 
degrees.  Since  it  turns  15  degree*  in  one  hour,  to  turn 
one  degree  it  will  require  1-15  of  an  hour  or  4  minutes 
of  time. 

Rotate  the  globe  from  west  to  east  until  the  pointer  L 
is  over  the  prime  meridian  ;  noon  now  takes  place  upon 
that  meridian  from  pole  to  pole.  Observe  that  all  places 
east  of  this  meridian  have  passed  the  sun  and  that  their 
noon  has  passed,  while  those  places  to  the  west  have  not 
yet  been  brought  to  the  sun,  and  their  noon  will  not  yet 
have  taken  place. 

EXAMPLE  1. 

When  it  is  noon  (12  o'clock)  at  Greenwich,  what  is  the 
time  in  Hamburg,  say  10  degrees  east  of  Greenwich  ? 
Hamburg  being  east  of  Greenwich  the  time  is  later  by 
the  time  required  by  the  earth  to  turn  10  degrees.  Since 
the  earth  turns  one  degree  in  4  minutes,  to  turn  10  de- 
grees will  require  10  times  4  minutes  or  40  minutes. 
The  difference  in  time  is  therefore  40  minutes,  and  since 
it  is  12  o'clock  at  Greenwich,  it  is  40  minutes  after  12  at 
Hamburg,  or  20  minutes  to  1  p.  M. 


38  LUNAR  TELLURIAN  MANUAL. 

EXAMPLE  2. 

When  it  is  noon  at  Greenwich  what  is  the  time  at  Rio 
Janeiro,  Brazil,  52  degrees  west  ? 

Rio  Janeiro  being  ivest  the  time  is  earlier  by  the  time 
required  by  the  earth  to  turn  52  degrees.  Since  the 
earth  turns  1  degree  in  4  minutes,  to  turn  52  degrees  will 
require  52  times  4  minutes,  or  208  minutes.  Reduced  = 
3  hours  28  minutes  ;  the  time  before  noon  at  Rio  Janeiro 
12  o'clock  noon  less  3  h.  28  min.  =  8  o'clock  32  min. 
A.  M.  the  time  at  Rio  Janeiro. 

EXAMPLE  3. 

When  it  is  11  o'clock  A.  M.  at  Hamburg  what  is  the 
time  at  Charleston,  S.  C.,  80  degrees  west  ?  Charleston 
being  west  the  time  is  earlier.  Charleston  is  80  degrees 
west  of  Greenwich  and  Hamburg  10  degrees  east,  the 
distance  between  Charleston  and  Hamburg  is  therefore 
80  degrees  +  10  degrees  =  90  degrees  ;  1  deg.  =  4  min. 
90  deg.  =  90  X  4  =  360  minutes,  reduced,  =  6  hours. 
11  o'clock  A.  M.,  less  6  hrs.  =  5  o'clock  A.  M. 

EXAMPLE  4. 

When  it  is  10  o'clock  A.  M.,  at  Constantinople,  28  de- 
grees east,  what  is  the  time  in  Hong  Kong,  112  degrees 
east  ?  Hong  Kong  being  112  degrees  east  and  Constan- 
tinople being  28  degrees  east,  the  distance  between  them 
is  112  deg.  less  28  deg.  =  84  deg.;  1  deg.  =  4  min.;  84 
deg.  =  84  X  4  =  336  min.;  reduced  =  5  hrs.  36  min. 
difference  in  time.  Hong  Kong  being  east,  the  time  there 
is  later  than  10  o'clock  A.  M.  by  5  hrs.  36  min. ;  10  hrs.  -f- 
5  hrs.  36  min.  =  15  hrs.  36  min.  or  as  commonly  read, 
3  hrs.  36  min.  p.  M. 


LUNAR  TELLURIAN  MANUAL.  39 

EXAMPLE  5. 

When  it  is  11. 30  A.  M.  at  San  Francisco,  122  cleg,  west, 
what  is  the  time  at  Melbourne,  Australia,  143  cleg,  east  ? 
Ans.  5  hrs.  10  min.  A.  M.  Observe  that  the  greatest 
longitude  a  place  can  have  is  180  deg.,  that  is,  half  way 
around  the  earth  from  the  prime  meridian.  If  a  person 
start  at  the  prime  meridian  and  go  west  he  will  be  in 
west  longitude  until  he  reaches  180  degrees,  when  his 
longitude  is  either  east  or  west.  If  he  proceed  on  his 
course  ten  degrees,  his  longitude  is  180  degrees  east,  less 
10  degrees,  or  170  East.  If  a  companion  had  gone  10 
degrees  east  his  longitude  would  be  180  degrees  west  less 
10  degrees,  or  170  West  ;  the  men  are  manifestly  20 
degrees  apart. 

To  Find  the  Difference  in  Longitude  Between  Two 
Places. 

1.  If  both  places  are  in  the  same  longitude  either  east 
or  west,  deduct  the  less  from  the  greater  and  the  result 
is  their  difference. 

2.  If  one  place  is  east  and  the  other  west,  the  sum  of 
their  longitudes  is  the  difference,  provided  the  sum  does 
not  exceed  180  degrees. 

3.  If  one  place  is  east  and  the  other  west,  and  the  sum 
of   their    longitudes    exceeds    180    degrees,  deduct    the 
amount  from  360  degrees,  and  the  remainder  is  the  differ- 
ence of  longitude  sought. 

Suppose  James  and  Howard  leave  the  prime  meridian, 
James  going  west  and  Howard  going  east  ;  when  each 
has  traveled  80  degrees  they  are  160  degrees  apart, 
which  is  their  difference  in  longitude,  Howard  being  east 
of  James.  Let  each  proceed  10  degrees  farther  and 


40  LUNAR  TELLURIAN  MANUAL. 

they  are  180  degrees  apart,  on  opposite  meridians,  How- 
ard being  either  east  or  'west  of  James.  Let  them  con- 
tinue in  their  course  10  degrees  ;  James  is  then  100 
degrees  west  and  Howard  100  degrees  east.  Together 
they  have  traveled  200  degrees,  and  as  360  degrees  are 
all  there  is  to  travel,  360  —  200  =  160,  the  number  of 
degrees  between  them,  Howard  being  now  160  degrees 
'west  of  James. 

Let  us  presume  they  started  on  their  journey  at  noon, 
and  that  they  carried  accurate  time  pieces  ;  when  they 
had  traveled  15  degrees  James  would  find  his  watch  an 
hour  too  fast,  and  to  correct  it  he  must  turn  it  back, 
while  Howard's  watch  is  found  to  be  an  hour  too  slow 
and  must  be  set  ahead.  To  keep  the  watches  right,  these 
changes  must  be  made  constantly,  James  turning  his 
watch  back  4  minutes  for  every  degree  traveled,  and 
Howard  setting  his  ahead  in  the  same  proportion.  When 
each  has  traveled  80  degrees  as  above,  and  it  is  noon  at 
the  prime  meridian,  James'  watch  shows  6  hrs.  40  min. 
A.  M.  (80  X  4  =  320  min.  =  5  hrs.  20  min.  subtracted 
from  12  noon  =  6  hrs.  40  min.  A.  M.)  and  Howard's 
watch  shows  5  hrs.  20  min.  p.  M.  When  each  has  trav- 
eled 90  degrees,  James  has  6  o'clock  A.  M.  and  Howard 
6  o'clock  P.  M.  when  it  is  noon  at  the  prime  meridian. 
When  each  has  traveled  179  degrees,  James'  watch  shows 
4  minutes  A.  M.,  and  Howard's  shows  11  hrs.  56  min.  p.  M. 
When  they  meet  at  180  degrees  their  watches  show  the 
same  hour,  12,  midnight.  James  has  gained  12  hours  by 
setting  his  watch  back,  while  Howard  has  lost  12  hours 
by  setting  his  ahead.  Though  both  watches  indicate  the 
same  hour  there  is  really  a  day's  difference  in  their  time. 
Were  they  quick-witted  Hibernians,  we  might  readily 


LUNAR  TELLURIAN  MANUAL.  41 

imagine  them  addressing  each  other  somewhat  like  this: 
Hello !  faix,  its  to-day  wid  me,  but  it's  yesterday  with  you. 
It's  nayther,  sir,  the  other  replies.  It's  to-day  wid  me 
and  to-morrow  wid  you. 

To  Find  the  Time  of  Sunrise  for  any  Place  or  any 
Day  in  the  Year. 

Arrange  the  globe  as  shown  in  Cut  No.  1.  Bring  the 
calendar  index  to  the  given  day,  rotate  the  globe  upon 
its  axis  until  the  given  place  is  under  the  western  edge 
of  the  day  and  night  circle  ;  place  the  time  index  H 
opposite  zero  on  the  equator  ;  tighten  the  screw  to  hold 
it  firmly  in  position.  Turn  the  globe  upon  its  axis  from 
west  to  east,  until  place  mentioned  is  opposite  the  pointer 
L  ;  note  on  the  equator  the  number  of  degrees  of  longi- 
tude that  has  passed  under  the  pointer,  reduce  the  longi- 
tude to  time  (as  directed  in  Longitude  and  Time,  page 
37).  The  result  is  the  time  from  sunrise  to  noon,  which 
subtracted  from  12  o'clock  noon,  gives  the  hour  of  sun- 
rise. 

EXAMPLES. 

1.  What  is  the  time  of  sunrise  at  Chicago,  May  1  ? 

2.  What  is  the  time  of  sunrise  at  New  Orleans,  June 
30,  1881. 

3.  What  is  the  time  of  sunrise   at    Melbourne,  Jan- 
uary 10  ? 

To  Find  the  Duration   of  Twilight  for   any  Place 
on  any  Day  in  the  Year. 

Arrange  the  globe  as  above.  Bring  the  calendar  in- 
dex  to  the  given  day,  and  the  given  place  to  the  begin- 
ning of  twilight.  Set  the  index  H  opposite  zero  on  the 
equator  ;  rotate  the  globe  upon  its  axis  until  the  given 


42  LUNAR  TELLURIAN  MANUAL. 

t 

place  is  carried  across  the  twilight  belt  ;  note  the  num- 
ber of  degrees  on  the  equator  the  globe  has  turned, 
which  reduce  to  time,  and  the  result  is  the  duration  of 
twilight  required. 

"EXAMPLES. 

1.  What  is  the  length  of  twilight  at  San  Francisco,, 
August  1  ? 

2.  What  is  the  length  of  twilight  at  Berlin,  June  21  ? 

The  Sun. 

The  sun  is  the  center  of  our  solar  system,  and  around 
him  all  the  planets  revolve  and  from  him  receive  their 
light  and  heat.  In  matter  he  is  750  times  greater  than 
all  the  planets  combined.  As  all  bodies  attract  each 
other  and  in  proportion  to  the  amount  of  matter  they 
contain,  so  the  sun's  attraction  must  be  750  times  greater 
than  the  combined  attraction  of  all  the  planets,  and  were 
they  all  to  unite  they  could  not  move  him  his  own 
diameter  from  the  center  of  gravity  of  our  solar  system. 
So  we  may  justly  regard  the  sun  as  the  center  of  gravity. 
The  attraction  of  the  sun  is  so  much  greater  than  the 
earth's,  that  a  boy  weighing  75  Ibs.  on  the  earth  would 
weigh  over  a  ton  if  placed  upon  the  sun. 

The  ancients  thought  the  sun  to  be  an  immense  globe 
of  iron  heated  to  a  white  heat.  While  this  is  not  liter- 
ally true,  it  shows  they  had  a  better  idea  of  the  sun  than 
of  the  earth,  which  they  thought  to  \>ejlat. 

The  apparent  diameter  of  the  sun  is  about  yz  a  de- 
gree— rather  more  than  less.  When  viewed  through  a 
powerful  telescope  his  surface  presents  a  mottled  appear- 
ance, which  Professor  Newcomb  likens  to  a  dish  of  rice 
soup  with  the  rice  grains  floating  upon  the  surface. 


LUNAR  TELLURIAN  MANUAL.  43, 

The  sun  seems  to  be  surrounded  by  a  very  rare,  light 
atmosphere,  principally  hydrogen  heated  to  a  glow,  in 
which  fleecy  cloucls  seem  to  float  ;  these  clouds  serve  to 
cut  off  from  us  some  of  the  fierce  light  and  heat  of  the 
sun,  and  were  it  not  for  these,  astronomers  tell  us  his 
light  and  neat  would  be  intolerable. 

The  prevailing  opinion  of  the  best  authorities  is,  that 
the  sun  proper  is  composed  of  condensed  gases  under 
great  pressure,  and  heated  to  a  temperature  many  times 
greater  than  furnace  heat. 

The  solar  spectrum  shows  the  presence  of  hydrogen, 
iron,  magnesium,  sodium  and  other  elements  in  the  sun  ;, 
but  of  what  the  sun  is  composed  we  know  very  little. 
His  extreme  brightness  renders  observations  very  diffi- 
cult. If  the  sun  were  placed  at  the  distance  of  the 
nearest  fixed  star  he  would  appear  no  larger  than  one  of 
the  smaller  stars. 

The  Sun  has  three  motions,  as  follows  : 

1.  A  rotation  upon  his  axis  once  in  25  days,  9^  hours. 

2.  A  revolution  around  the   center  of  gravity.     This 
movement  is  very  slight. 

3.  A  revolution    around  some   distant  and  unknown 
center,  carrying  with  him  the  entire  solar  system  at  a  rate 
of  20,000  miles   an    hour,  and  traveling  in  an  orbit  so 
great  that  to  make    one    complete    revolution    requires 
about  eighteen  million  years!     This  is  perhaps  the  most 
astounding  of  all    astronomical    movements,    and    the 
question  "  Whither  are  we  going  ?"  may  well  be  asked  I 


44  LUNAR  TELLURIAN  MANUAL. 


The  Earth. 

The  Earth  is  one  of  the  eight  principal  planets.  She 
ranks  fifth  in  size,  and  third  in  her  distance  from  the  sun, 
Her  distance  varies  between  91  and  94  million  miles. 
She  has  at  least  eight  distinct  motions,  but  some  of  them 
it  is  not  our  province  to  consider  in  this  work.  Among 
the  simpler  and  better  understood  of  the  number  are  : 

1.  Rotation  upon  her  axis  every  24  hours. 

2.  Revolution  around  the  sun  annually  in  an  Elliptical 
orbit. 

3.  Revolution  of  the  equator  around  the  pole   of  the 
Ecliptic.     (See  Precession  of  the  Equinoxes.) 

The  Earth's  surface  is  divided  into  solid  and  liquid, 
there  being  about  3-10  of  the  former  and  7-10  of  the 
latter.  The  solid  we  call  land  and  the  liquid  water.  The 
crust  and  liquid  covering  of  the  earth  as  compared  with 
her  size  is  very  thin,  probably  not  a  hundred  miles  thick, 
and  if  shown  upon  the  globe  the  crust  would  be  reduced 
to  the  thickness  of  thin  cardboard !  This  crust  is  sup- 
posed to  float  on  the  molten  fiery  interior  of  the  earth. 
Among  the  proofs  that  the  interior  of  the  earth  is  a  sea  ot 
fire,  are  the  following  : 

1.  As  we  go  down  into  the  solid  crust  of  the  earth  the 
temperature  rises  at  nearly  the  uniform  rate  of  1  degree 
for  every  50  feet  we  descend.  At  a  distance  of  less  than 
2  miles,  water  would  boil;  at  a  depth  of  10  miles,  the 
crust  would  be  red-hot.  Below  the  surface,  90  to  100 
miles,  the  temperature  would  be  sufficient  to  melt  any 
substance  known  to  man. 


LUNAR  TELLURIAN  MANUAL.  45 

2.  In    various   parts    of  the    earth's   surface  we   find 
springs  of  hot  water  boiling  up  out  of  the  earth's  crust, 
and  we  know  of  no  way  the  water  could  be  heated  except 
by  the  internal  fires  of  the  earth. 

3.  Volcanoes,  that  seem  to  act  as  safety  valves,  through 
which  the  Furies  of  the  pent  up  fires  find  relief  in  send- 
ing forth  fire,  gases  and  lava.     The   latter  is  composed 
of  well-known   substances,   such  as   rock  and  minerals 
melted  to  a  liquid  form. 

4.  The  form  of  the  earth   flattened  at  the  poles  and 
bulged  out  at  the  equator,  shows  that  the  earth  in  her 
childhood  (if  we  may   be    allowed  the  term),  must  have 
been  in  a  soft,  pliable  state,  in  which  case  the  earth  would 
necessarily  assume  the   form  she  now  has.     From  what 
we  know  of  the  interior  of  the  earth   it  could  not  have 
been  in  this  soft  plastic  state  except  by  the  action  of  heat. 
Geological    formations   show  evidences  of  great  heat  at 
some  former  period  of  the  earth's  existence. 

The  Moon. 

The  Moon's  Form,  Size  and  Physical  Condition. 

The  moon,  like  the  earth,  is  very  nearly  round.  Her 
diameter  is  2,160  miles,  and  her  volume  is  about  1-49  the 
size  of  the  earttu  and  only  ^^fa^^  times  the  size  of 
the  sun.  The  moon,  to  us,  appears  nearly  as  large  as 
the  sun.  This  is  because  she  is  about  400  times  nearer 
to  us.  A  ball  thrown  high  in  the  air  seems  smaller  than 
when  tossed  up  but  a  few  feet.  Thus  we  see  the  appar- 
ent size  of  bodies  depends  largely  upon  their  distance 
from  us. 


46  LUNAR  TELLURIAN  MANUAL. 

The  moon,  as  seen  through  a  telescope,  presents  a  very 
uneven  and  broken  surface,  showing  very  high  moun- 
tains, deep  valleys,  and  the  craters  of  immense  volcanoes 
now  extinct.  The  clouded  or  mottled  appearance  of  its 
surface  sometimes  called  "  The  man  in  the  moon,"  and 
which  many  ignorant  people  think  to  be  land  and  water, 
is  really  due  to  the  difference  in  the  reflecting  power  of 
the  various  portions  of  the  moon's  surface.  The  higher 
portions  of  her  surface  seem  to  be  composed  of  lighter 
colored  material  than  the  lower,  and  they  will  therefore 
reflect  more  light  than  the  darker  colored  and  lower  sur- 
face. If  examined  through  a  small  telescope  or  field 
glass,  we  are  able  to  see  some  spots  on  the  lighter  sec- 
tions brighter  than  the  surrounding  surface  ;  these  are 
the  summits  of  mountains,  the  most  prominent  being 
craters  of  volcanoes.  The  most  careful  observations  of 
the  moon  fail  to  show  any  atmosphere.  There  can  be 
no  water,  for  the  sun's  heat  during  the  long  lunar  days 
(about  a  month  long)  would  evaporate  it  and  produce  a 
cloud-like  film  around  the  moon  that  could  readily  be 
seen. 

The  results  of  observations  upon  the  physical  condi- 
tions of  the  moon  are  such  that  we  must  conclude  that 
it  is  a  cold,  lifeless  body,  the  essential  elements  of  life, 
air  and  water,  not  being  found. 

The  Moon's  Motions. 

The  moon  has  three  positive  motions. 

1.  A  revolution  on  her  axis  once  in  29  ^  days.  Thus 
we  see  the  lunar  day  is  29^  times  longer  than  the  terres- 
trial. To  an  observer,  on  the  moon  near  its  equator,  the 
sun  would  rise  in  the  east  and  set  in  the  west  ;  but  the 


LUNAR  TELLURIAN  MANUAL.  47 

period  of  time  between  sunrise  and  sunset  would  be  equal 
to  nearly  15  of  our  terrestrial  days,  and  when  the  sun 
had  set  it  would  not  rise  for  an  equal  period.  How  great 
must  be  the  extremes  of  temperature  !  The  lunar  day 
must  be  hotter  than  anything  experienced  upon  the 
•earth,  while,  during  the  lunar  night  the  temperature  must 
fall  to  a  degree  unknown  save  In  the  polar  latitudes  of 
our  earth.  To  an  observer  on  the  moon,  the  earth  would 
look  like  a  huge  moon  13  times  larger  than  the  moon 
appears  to  us.  It  would  present  the  phases  of  the  moon 
as  we  see  them,  but  on  a  grander  scale.  Owing  to  the 
moon's  slow  axial  rotation,  the  earth  would  not  appear  to 
revolve  around  it,  but  merely  swing  back  and  forth 
through  a  few  degrees. 

2.  A  revolution  around  the  earth  once  in  27 1/3  days. 

3.  A  revolution  with  the  earth  around  the  sun  annu- 
ally.    The    result  of  the    last   two    motions    makes  the 
actual  path  of  the  moon  very  peculiar.     The  second  mo- 
tion mentioned,  of  itself,  would  carry  the  moon  around 
the  earth  so  that  its   path    would   be   an    ellipse  ;  while 
however,  this  movement  is  going  on,  the  last  mentioned 
movement  (No.  3)   is  also  in  operation  and  is  about  30 
times  as  rapid  as  the  former  (No.  2),  making    the  actual 
path  an  irregular  curve,  sometimes    outside    and  some- 
times inside  the  earth's  orbit;  but  its  path  always  curves 
to  the  sun.     The  moon's  orbital  velocity  is  about  2,300 
miles  per  hour,  while  she  follows  the  earth  in  her  great 
orbital  journey  at  the  rate  of  68,000  miles  an  hour — over 
a  thousand  miles  a  second* 

If  the  earth  were   at  rest  in  her  orbit  the  path  of  the 
moon  would  be  similar  to    cut  No.  1,  (E    the    earth,  M 


LUNAR  TELLURIAN  MANUAL. 


the  moon,  the  arrows  showing  the 
direction  of  the  moon's  revolu- 
tion); Since  the  earth  is  not  at  rest, 
cut  No.  1  shows  the  relative  and  not 
the  true  path  of  the  moon. 


Let  A  in  cut  2  represent  part  of 
the  orbit  of  the  earth,  arid  E  B  F 
will  show  the  true  path  of  the 
moon  from  her  last  to  her  first 
quarter,  or  while  traveling  from 
O  to  P,  as  shown  in  cut  1.  The 
moon  makes  this  path  because 
she  is  carried  forward  with  the 
earth  around  the  sun  from  F  to  E 
while  she  is  revolving  around  the 
earth  from  O  to  P,  cut  1.  If  the 
moon's  path  from  F  to  E  were  on 
the  line  G  H,  she  would  neither 
curve  to  nor  from  the  sun,  but  be 
traveling  on  a  straight  line  and  at 
right  angles  to  him.  If  this  were 
true,  at  the  point  J,  she  would  be 
over  400,000  miles  from  the  earth 
then  at  I,  but  as  the  moon's  dist- 
tance  is  about  240,000  miles,  she 
must  be  at  K  instead  of  J.  Hence, 
the  moon's  path  must  be  on  the 
line  E  B  F,  which  is  concave  to, 
or  curving  towards  the  sun.  After 
passing  the  point  E  the  moon's 
orbit  curves  sharply  in,  and  in  14 


CUT  No.  i. 


LUNAR  TELLURIAN  MANUAL.  49 

days  crosses  to  the  inside  of  the  earth's  orbit,  as  we  ob- 
serve it  does  at  the  point  F. 

The  Sidereal  and  Synodic  Revolutions  of  the  Moon. 

The  moon  revolves  around  the  earth  in  an  elliptical 
orbit  once  in  27 1/3  days  ;  this  is  called  the  sidereal  revo- 
lution. Sidereal  means  Star. 

Ask  the  pupils  to  observe  that  as  the  moon  ball  re- 
volves around  the  globe  it  is  nearer  the  globe  when  on 
one  side  of  it  than  when  upon  the  other.  In  like  manner 
the  moon  revolves  around  the  earth  ;  sometimes  she  ap- 
proaches within  221,000  miles  of  the  earth.  Her  great- 
est distance  is  259,000.  She  seldom  reaches  these  ex- 
treme limits  ;  her  usual  variations  are  about  13,500  miles 
either  way  from  the  average,  which  is  about  240,000  miles. 

Ask  the  pupils  to  observe  the  position  of  the  moon 
and  some  star  near  it  in  the  heavens  ;  on  the  following 
evening  the  moon  will  have  moved  some  distance  to  the 
eastward  ;  continue  the  observations  through  several 
evenings,  and  note  the  changes  of  the  moon's  position 
in  the  stars.  In  27^  days  (about)  the  moon  will  have 
passed  clear  around  the  heavens  and  will  again  appear 
near  the  star  where  it  wras  first  observed.  The  moon  has 
now  made  one  sidereal  revolution  (one  revolution  as  re- 
gards the  stars).  If  the  sun  and  not  a  star  were  taken 
for  the  base  of  the  observation,  the  time  required  for  the 
moon  to  revolve  around  the  earth  and  be  brought  to  its 
former  position  relative  to  the  sun  would  be  29^  days, 
about.  This  is  a  synodical . revolution. 

Call  the  pupil's  attention  to  the  fact  that  the  sun  ap- 
parently travels  from  west  to  east  through  the  heavens, 
going  clear  around,  or  3GO  degrees  in  a  year  (about  365 


50  LUNAR  TELLURIAN  MANUAL. 

days),  and  of  course  must  travel  on  an  average  nearly  a 
degree  a  day.  The  moon  makes  a  complete  revolution 
through  the  heavens  in  27^  days,  or  about  13  degrees 
daily,  and  in  the  same  direction  that  the  sun  apparently 
travels.  Let  us  suppose  the  sun,  the  moon  and  a  star  to 
•be  in  line  on  a  given  day  ;  on  the  day  following,  if  ob- 
served, the  sun  will  be  seen  about  1  degree  east  of  the 
star,  and  the  moon  will  be  seen  about  13  degrees  east  of 
the  star  and  12  degrees  east  of  the  sun.  The  following 
day  the  sun  will  be  about  2  degrees  east  of  the  star  and 
the  moon  will  be  about  26  degrees  east  of  the  star  and 
24  degrees  from  the  sun.  Observe  that  at  this  rate  the 
moon  will  be  27 y$  days  in  passing  around  the  earth  and 
again  getting  into  line  with  the  star,  thus  completing  the 
sidereal  revolution.  The  sun  in  the  mean  time  has  passed 
to  about  27  degrees  east  of  the  star,  and  for  the  moon  to 
overtake  him  will  require  about  2  1-6  days  additional, 
thus  completing  the  sy nodical  revolution  in  29^  days. 
The  change  of  the  moon  depends  upon  its  relation  to  the 
sun  and  not  to  a  star,  so,  from  one  new  moon  to  another 
is  29^  days  (about). 

The  Phases  of  the  Moon. 

The  moon  shines  by  reflected  sunlight  ;  like  the  earth, 
one-half  of  her  surface  is  illuminated  by  the  sun,  and 
when  any  part  of  the  light  hemisphere  is  turned  toward 
the  earth,  we  see  that  portion  brightly  illuminated,  and 
the  light  it  gives  us  we  call  moonlight.  The  moon  acts 
as  a  great  heavenly  mirror  reflecting  the  sun's  light  after 
he  is  gone.  The  bright  side  of  the  moon  is  of  course 
always  toward  the  sun. 

The  Dark  Moon. 
the  pupils   to   notice  that  when  the  moon  is  be- 


LUNAR  TELLURIAN  MANUAL.  51 

tween  the  earth  and  suri,  the  light  hemisphere  of  the 
moon  must  be  hid  from  the  earth.  Astronomically  we 
say  the  moon  and  sun  are  in  conjunction  ;  as  ordinarily 
expressed,  we  say  it  is  the  "  Dark  of  the  Moon  "  or  "  No 
Moon."  Pemonstrate  this  by  the  apparatus. 

• 
New  Moon- 

Move  the  globe  forward  in  the  orbit  until  the  moon 
has  passed  two  or  three  inches  to  the  east  of  the  pointer 
L.  Ask  the  pupils  to  observe  that  the  moon  is  not  now 
between  the  globe  and  the  arc  S,  but  has  passed  to  the 
eastward,  and  that  now  the  hemisphere  seen  from  the 
globe  has  a  crescent  of  light  around  the  western  part  and 
that  the  "  Horns  of  the  Moon  "  or  the  ends  of  the  cres- 
cent point  eastward.  We  say  the  moon  is  now  new,* 
and  being  but  little  east  of  the  sun,  sets  soon  after  him. 
At  new  moon  when  the  air  is  clear  we  can  plainly  see 
the  outline  of  the  dark  hemisphere.  When  the  moon  is 
situated  nearly  between  the  earth  and  sun  as  at  new 
moon,  the  bright  or  illuminated  hemisphere  of  the  earth 
is  towards  the  moon.  Show  this  upon  the  apparatus 
mounted  as  in  cut  No.  1.  An  observer  on  the  moon's 
dark  hemisphere  would  now  have,  if  we  may  be  allowed 
the  term,  earthlight,  in  character  similar,  though  in 
quantity  greater  than  the  light  we  receive  from  the  moon 
when  it  is  full.  The  sunlight  reflected  by  the  earth  to 
the  moon  is  in  a  diminished  quantity  re-reflected  by  her 
to  the  earth,  and  by  this  light  twice  reflected  we  see 

*Infact  the  moon  the  moment  she  passes  between  the  earth 
and  sun,  or  reaches  conjunction,  becomes  "  new,"  though  she  is 
not  usually  called  new  until  the  crescent  is  visible.  Hereafter,  in- 
this  work  New  Moon  means  Conjunction. 


LUNAR  TELLURIAN  MANUAL. 


dimly  the  moon's  dark  hemisphere.  The  reason  why 
the  moon's  crescent  is  brighter  than  the  dark  hemisphere, 
is  because  the  light  coming  from  it  is  reflected  but  once, 
while  that  from  the  dark  hemisphere  is  reflected  twice, 
the  difference  in  brilliancy  showing  the  loss  by  the  second 
reflection. 

When  new  moon  occurs  while  the  moon  is  above  the 
ecliptic,  as  shown  in  cut  No.  1,  the  moon  will  be  above 
as  well  as  east  of  the  sun,  and  her  crescent  must  appear 
lower  than  when  she  is  below  the  ecliptic.  Thus  we  have 
what  is  called  the  "  dry  "  and  "  wet  "  moon. 

First  Quarter. 

Move  the  arm  IX  forward  until  the  moon  ball  has 
passed  one-fourth  of  the  way  around  the  globe  from  the 
arc  S.  To  an  observer  on  the  globe  the  crescent  of  light 
during  this  movement  will  have  increased  until  now  one- 
half  of  the  illuminated  hemisphere  is  in  view.  The 
moon  is  now  one-quarter  of  the  way  around  the  earth 
from  the  sun,  and  is  in  quadrature.  The  moon  is  now 
in  her  first  quarter. 

Full  Moon. 

Move  the  arm  IX  forward  until  the  moon  ball  has 
passed  one-half 'the  way  around  the  globe,  and  call  the 
pupil's  attention  to  the  fact  that  an  observer  upon  the 
earth  would  see  the  entire  illuminated  hemisphere  of  the 
moon,  and  that  as  she  is  almost  directly  opposite  the  sun 
she  must  rise  at  or  near  sunset.  The  moon  is  now  in 
opposition  with  the  sun  and  we  have,  illustrated,  the 
phase  of  the  moon  called  the  Full  Moon. 


LUNAR  TELLURIAN  MANUAL.  53 

Last  Quarter. 

Move  the  arm  IX  forward  until  the  moon  ball  has 
passed  three-fourths  of  the  way  around  the  globe  and  ask 
the  pupils  to  observe,  as  this  is  done,  that  the  illuminated 
hemisphere  of  the  moon  shifts  to  the  eastward  so  that 
when  it  is  brought  to  the  three-quarter  position  only  one- 
half  of  it  is  visible  to  an  observer  upon  the  globe.  The 
moon  is  again  in  quadrature  with  the  sun,  and  presents 
the  phase  of  the  moon  in  her  last  quarter, 

Old  Moon. 

Move  the  arm  IX  until  the  moon  ball  is  brought  about 
half  way  between  the  last  quarter  and  the  dark  of  the 
moon,  and  observe  that  a  crescent  of  light  may  be  seen 
around  the  eastern  side  of  the  moon,  the  horns  of  the 
crescent  pointing  to  the  west.  The  moon  is  now  "  old," 
from  which  position  she  passes  to  conjunction  and  the 
dark  moon,  thus  completing  the  common  phases  of  the 
moon. 

The  Orbit  of  the  Moon. 

The  orbit  of  the  moon  is  an  ellipse,  her  least  distance 
from  the  earth  is  221,000  miles,  while  her  greatest  dis- 
tance is  259,000  miles.  She  seldom,  however,  reaches 
these  extreme  limits,  her  usual  variations  from  her  mean 
distance  of  240,000  miles,  being  about  13,500  miles  each 
way.  The  orbit  of  the  moon  crosses  the  orbit  of  the 
earth  at  an  angle  a  little  greater  than  5  degrees.  This 
is  shown  (somewhat  exaggerated)  by  plate  E  on  the 
globe,  which  carries  the  moon  ball  in  an  inclined  orbit 
above  and  below  the  ecliptic.  The  moon's  declination  is 
her  distance  north  or  south  of  the  ecliptic.  In  cut  No.  1 


54  LUNAR  TELLURIAN  MANUAL. 

the  moon  is  shown  above  the  ecliptic  in  her  greatest 
northern  declination.  In  cut  No.  2  she  is  shown  below 
the  ecliptic  in  her  greatest  southern  declination. 

The  Moon's  Nodes. 

The  nodes  of  the  moon  are  the  two  points  where  her 
orbit  cuts  or  crosses  the  ecliptic.  The  node  where  the 
moon  crosses  the  ecliptic  coming  north  is  called  her 
ascending  node,  and  the  opposite  one  the  descending 
node. 

The  pupils  should  fix  clearly  the  moon's  nodes  in  their 
minds,  as  upon  this  depends  the  understanding  of  much 
that  is  to  follow. 

If  the  sun  and  moon  could  leave  a  thread  of  light  to 
mark  their  pathway  through  the  heavens  (the  sun's  ap- 
parent annual  path),  we  would  observe  these  lines  run- 
ning very  near  each  other  and  to  cross  at  opposite  points 
of  the  heavens,  so  that  as  viewed  from  the  earth  the  path 
of  the  sun  would  sometimes  be  above,  and  sometimes 
below  the  path  of  the  moon,  crossing  it  at  opposite  points 
— the  moon's  nodes.  These  points  of  crossing  are  not 
fixed,  but  are  constantly  changing,  falling  back  to  the 
westward  on  the  ecliptic  or  sun's  apparent  path  about  20 
degrees  annually.  If  the  nodes  were  stationary,  then 
the  time  required  by  the  sun  to  pass  from  one  ascending 
node  to  another,  manifestly,  would  be  a  year.  Because 
of  the  moon's  nodes  revolving  backward  on  the  ecliptic 
about  20  degrees  annually,  he  will  approach  her  nodes 
about  19  days  earlier  than  he  otherwise  would.  Dis- 
carding fractions  we  have  :  1  year,  365  days,  less  19  days 
=  346  days  the  time  required  by  the  sun  to  pass  from 
one  ascending  node  to  another.  As  the  descending  node 


LUNAR  TELLURIAN  MANUAL.  55 

occurs  midway  between  two  ascending  nodes,  we  have 
346  days  -r-  2  =  173  days  as  the  time  from  the  ascending 
to  the  descending  node,  and  an  equal  period  from  the 
descending  to  the  ascending  nodes. 

Move  the  arm  IX  until  the  mooii  ball  is  between  the 
globe  and  the  arc  S,  turn  the  plate  E  to  the  right  until 
the  center  of  the  moon  ball  is  opposite  the  pointer  L ;  the 
sun  and  moon  are  now  at  the  node.  Note  the  day  of  the 
month  under  the  calendar  index  G.  Move  the  arm  IX 
forward  carrying  the  globe  around  the  arc  S  to  its  former 
position  and,  at  the  same  time,  turn  the  plate  E  about 
1-18  the  way  around  in  the  opposite  direction,  and  ob- 
serve the  sun  has,  because  of  this  change  in  the  position 
of  the  moon's  orbit,  passed  the  moon's  node  about  19 
days  earlier  than  he  would  have  done  had  the  moon's  orbit 
not  changed  position- 

The  Zodiacal  Belt. 

The  Zodiacal  Belt  is  a  band  in  the  heavens  lying  8 
degrees  on  either  side  of  the  ecliptic,  in  which  the  sun, 
moon  and  the  principal  planets  are  seen  to  move.  All 
the  planets  go  around  the  sun  in  the  same  general  direc- 
tion, from  west,  to  east.  The  orbit  of  the  earth,  the 
ecliptic,  is  the  base,  and  from  it  the  inclinations  of  the 
orbits  of  the  several  planets  are  measured.  None  of  the 
orbits  of  principal  planets  cross  the  orbit  of  the  earth  at 
an  angle  greater  than  8  degrees  and  most  of  them  cross 
at  an  angle  considerably  less.  If  all  the  planets  could 
leave  behind  them  a  thread  of  light  to  mark  their 
pathway  through  the  heavens,  we  would  see  that  within 
a  belt  of  the  heavens  16  degrees  wide,  lying  8  degrees 
on  either  side  of  the  ecliptic,  would  lie  the  orbits  of  all 


56  LUNAR  TELLURIAN  MANUAL. 

the  principal  planets,  and  in  this  belt  they  would  be  seen 
to  move.  This  band  or  zone  of  the  heavens  is  called 
«  The  Zodiacal  Belt." 

The  Signs  of  the  Zodiac. 

The  ancient  astronomers  for  some  reason  not  now  well 
known,  divided  the  Zodiacal  Belt  into  twelve  equal  parts 
of  thirty  degrees  each,  giving  to  each  sign  a  name,  be- 
ginning with  the  vernal  equinox  or  the  equinoctial  col- 
ure,  counting  thirty  degrees  east  and  naming  this  "sign" 
44 Aries;"  to  the  next  thirty  degrees  east  they  gave  the 
name  "Taurus,"  so  continuing  in  the  order  shown  upon 
the  base  of  the  globe.  Thus  we  see  that  a  "Sign  of  the 
Zodiac"  is  a  portion  of  the  heavens  having  a  longitude 
or  length  of  30  degrees  and  a  latitude  or  breadth  of  16 
degrees. 

Passage  of  the   Moon    Through   the   Signs   of  the 
Zodiac. 

We  learned  upon  the  previous  page  that  the  moon  had 
her  revolution  in  the  Zodiacal  Belt,  and  as  she  passes 
clear  around  the  heavens,  360  degrees,  in  making  her 
sidereal  revolution,  she  must  in  that  time  have  passed 
once  through  all  the  Signs  of  the  Zodiac.  If  the  moon 
passes  through  the  12  Signs  of  the  Zodiac  in  27  ^  days, 
(a  sidereal  revolution),  she  will  occupy  about  2*^  days  in 
passing  through  one  sign. 

Rotate  the  globe  upon  its  axis  until  the  ecliptic  marked 
on  the  globe  lies  in  a  horizontal  plane.  If  you  were  to 
take  a  large  and  wide  barrel  hoop  and  place  it  around 
the  entire  apparatus  and  hold  it  in  such  a  position  that 
the  plane  of  the  ecliptic  extended  to  the  hoop  it  would 
strike  the  middle  of  the  hoop  all  the  way  around  it;  the 


LUNAR  TELLURIAN  MANUAL.  57 

hoop  would  then  show  the  position  of  the  Zodiacal 
Belt  for  the  Lunar  Tellurian.  Or,  if  the  apparatus  were 
placed'in  a  large  tub,  and  water  were  poured  in  until  one- 
half  of  the  globe  ball  only  remained  above  the  water, 
the  surface  of  the  water  would  be  the  plane  of  the  eclip- 
tic, and  that  portion  of  the  tub,  say  2  inches  above  and 
2  inches  below  that  surface  would  represent  the  Zodi- 
acal Belt.  If  the  tub  were  made  of  twelve  wide  staves, 
each  stave  would  represent  a  "  Sign  of  the  Zodiac."  Let 
the  globe  move  forward  in  her  orbit,  and  the  moon  would 
be  seen  by  an  observer  upon  the  globe,  to  pass  through 
these  signs  upon  the  staves  from  west  to  east,  as  the 
moon  in  the  heavens  actually  does  pass  through,  or  by 
the  Signs  of  the  Zodiac. 

When  we  say  the  moon  is  in  Aries,  we  mean  that  the 
moon  as  seen  from  the  earth  is  in  that  sign,  or  more  prop- 
erly, between  us  and  that  part  of  the  Zodiacal  Belt  called 
the  sign  Aries.  A  very  instructive  and  interesting  illus- 
tration may  be  given  by  placing  the  Lunar  Tellurian 
upon  a  table  and  having  the  pupils,  twelve  in  number, 
join  hands  around  it.  Let  each  one  take  the  name  of  the 
sign  nearest  to  him  on  the  base  of  the  globe.  Move  the 
arm  IX  forward,  and  when  the  moon  ball,  in  passing 
around  the  globe,  comes  between  the  globe  and  one  of 
the  pupils,  let  that  pupil  speak  the  name  of  the  sign  he 
represents  ;  thus,  Mary  will  say,  when  the  moon  ball  is 
opposite  her,  "Aries;"  in  a  moment  it  has  passed  Mary 
and  is  opposite  John,  who  calls  out,  "  Taurus,"  and  so  on 
through  the  twelve  signs.  Where  the  pupils  join 
hands  will  mark  the  divisions  of  the  signs. 

The  writer  strongly  urges  the  use  of  the  above  illus- 
tration, for  by  it  the  children,  though  quite  small,  will  get 


58  LUNAR  TELLURIAN  MANUAL. 

a  very  clear  conception  of  the  Zodiacal  Belt,  the  signs  of 
the  Zodiac  and  the  way  the  moon  passes  through  these 
signs. 

Passage  of  the  Sun  Through  the  Signs  of  the  Zodiac 

The  sun  passes  through  the  signs  of  the  Zodiac  in  a. 
manner  very  similar  to  the  moon,  and  the  illustrations 
used  to  show  the  passage  of  the  moon  through  the  signs 
may  be  used  to  equal  advantage  to  show  the  sun's  pass- 
age. The  sun  passes  through  the  twelve  signs  once 
every  year  and  so  occupies  about  one  month  in  passing 
each  sjgn.  The  pointer  G,  cut  No.  1,  shows  at  all  sea- 
ST  ns  of  the  year  the  sign  and  the  degree  of  the  sign 
where  the  sun  is  situated.  Thus,  at  the  vernal  equinox 
we  see  the  sun  is  in  the  first  degree  of  the  sign  Aries. 
Move  the  arm  IX  forward  to  June  21,  and  observe  that 
in  the  mean  time  the  sun  has  passed  through  the  signs 
Aries,  Taurus  and  Gemini,  and  has  reached  the  sign 
Cancer. 


KoTE.When  studying  the  change  of  seasons  we  saw  that  on  June  2ist  the 
sun  reached  its  greatest  northern  limit  23^  degrees  north  of  the  equator,  from 
which  position  it  turned  southward  towards  the  equator.  Thus  we  see  the  sun 
turns  south  at  the  moment  he  reaches  the  sign  Cancer.  We  derive  the  word 
"Tropic"  from  the  Greek  word  trepo,  which  means  to  turn.  The  word  Cancer 
shows  the  position  of  the  sun  "when  it  turns  southward,  and  from  a  union  of 
these  two  we  get  "Tropic  of  Cancer."  The  same  is  true  of  the  turning  of  the 
sun  northward  on  December  22d,  as  it  reaches  the  sign  Capricornus,  thereby 
giving  us  "Tropic  of  Capricorn.'1 

Passage   of  the    Earth    Through   the   Signs  of  the 
Zodiac. 

The  earth  is  always  said  to  be  in  the  sign  directly  op- 
posite the  one  where  the  sun  is  situated.  Thus,  when  the 
sun  is  in  Cancer  the  earth  is  said  to  be  in  Capricornus, 


LUNAR  TELLURIAN  MANUAL.  59 

where  it  would  be  seen  by  an  observer  upon  the  sun's 
surface. 

Eclipses. 

An  eclipse  in  general,  is  the  cutting  off  in  whole  or  in 
part  the  sunlight,  as  it  falls  upon  the  earth  or  moon. 
All  the  planets  are  opaque  ;  they  absorb  in  part  the  sun- 
light that  falls  upon  them,  and  the  remainder  after  ab- 
sorption is  reflected  back  into  space.  No  light  passes 
through  them.  They  cast  shadows  into  space,  the  extent 
of  these  shadows  depending  upon  the  size  of  the  planet 
and  its  distance  from  the  sun.  The  larger  the  planet  the 
larger  the  shadow,  and  the  farther  the  planet  is  from  the 
sun  the  farther  the  shadow  will  extend  into  space.  To 
illustrate  this,  draw  a  circle  on  the  blackboard  a  foot  in 
diameter  to  represent  the  sun,  mark  this  circle  S  ;  two 
feet  from  this  circle  draw  a  small  circle,  say  three  inches 
in  diameter,  mark  this  circle  E  to  represent  the  earth. 
Draw  a  straight  line  from  the  top  of  circle  S  to  the  top 
of  circle  E,  continue  the  line  a  foot  or  more  beyond  E  ; 
next,  draw  a  line  from  the  bottom  of  circle  S  to  the  bot- 
tom of  circle  E,  and  continue  this  straight  line  until  it 

*  O 

crosses  the  other  line  ;  the  distance  from  where  these 
lines  cross,  to  the  circle  E,  represents  the  distance  the 
shadow  of  the  earth  would  extend.  Draw  another  three 
inch  circle,  say  four  feet  away  from  circle  S,  and  draw 
similar  straight  lines  from  top  to  top  and  bottom  to  bot- 
tom- of  the  circles,  extending  them  as  in  the  other  illus- 
tration, and  ask  the  pupils  to  observe,  that  now  the  dis- 
tance from  the  crossing  of  the  lines  to  the  circle  E  is 
greater  than  in  the  first  instance  when  the  circles  were 
closer  together.  Thus  we  see  that  the  nearer  a  body 
of  a  given  size  is  to  the  sun  the  shorter  will  be  its  shadow, 


66  LUNAR  TELLURIAN  MANUAL. 

and  the  farther  it  is  from  the  sun  the  longer  will  it  ex- 
tend. Draw  a  straight  line  from  the  center  of  circle  S 
through  the  center  of  circle  E,  and  extend  it  until  it 
reaches  the  crossing  of  the  two  lines  before  mentioned, 
and  ask  the  pupils  to  observe  that  the  line  last  drawn 
may  represent  the  ecliptic,  and  that  it  divides  the  shadow, 
into  two  equal  parts,  one- half  of  which  is  above  and  one- 
half  below  it.  So  the  earth  into  space  casts  her  shadow, 
equal  parts  of  which  lie  above  and  below  the  ecliptic. 
Thus  we  see  : 

(a)  That  the  shadows  cast  by   any  planet,  great  or 
small,  must  lie  in  the  plane  of  that  planet's  orbit. 

(b)  That  the  shadows   cast   by  the  planets  are  in  the 
shape  of  a  cone  tapering  to  a  point,  the  base  of  the  cone 
being  equal  in  diameter   to   the   diameter  of  the  planet, 
the  distance  to  the  point  or  frustum  of  the  cone  depend- 
ing upon  the  distance  of  the  planet  from  the  sun. 

(c)  That  the  diameter  of  the  shadow  at  any  point  de- 
pends upon    the   distance   of  that   point   from  the  body 
casting  the  shadow. 

The  cone-shaped  shadow  of  the  planet  is  called  its 
umbra,  and  to  an  observer  situated  in  the  umbra  the  sun 
is  wholly  obscured  and  to  him  the  eclipse  is  total.  Place 
the  observer  just  outside  of  the  umbra  and  the  sun  is  not 
wholly  obscured  to  him  ;  his  situation  is  now  in  pen- 
umbra. To  show  the  penumbra  take  the  figures  upon 
the  blackboard  used  to  show  the  umbra,  and  in  addition 
draw  a  straight  line  from  the  bottom  of  circle  S  through 
the  top  of  circle  E  and  extend  it  a  foot  or  two  beyond. 
Draw  another  straight  line  from  the  top  of  circle  S 
through  the  bottom  of  circle  E  and  extend  it  as  before, 


LUNAR  TELLURIAN  MANUAL.  61 

the  space  beyond  the  circle  E  on  either  side  of  the  umbra 
and  between  it  and  the  lines  last  drawn  shows  the  pen- 
umbra. The  shadows  of  all  heavenly  bodies  must  have 
umbra  and  penumbra. 

Umbra  means*  totality,  and  penumbra,  partiality. 
The  Dimensions  of  the  Earth  and  Moon's  Umbra. 

The  length  of  the  earth's  umbra  is  about  860,000 
miles,  or  about  3^  times  farther  than  the  moon  is  from 
the  earth.  This  is  the  average  length :  in  December  arid 
January  (because  then  near  the  sun)  the  umbra  is  about 
843,000  miles,  while  in  June  and  July  (when  farthest 
away)  her  umbra  is  nearly  872,000  miles.  The  diameter 
of  the  earth's  umbra  at  the  distance  of  the  moon  is  on 
an  average  about  6,000  miles,  nearly  three  times  the 
moon's  diameter. 

The  average  length  of  the  moon's  umbra  is  236,000 
miles.  It  varies,  however,  from  221,150  to  252,640  miles. 
Observe  that  the  average  length  of  the  moon's  umbra  is 
a  little  less  than  her  average  distance  from  the  earth 
(240,000  miles).  Therefore,  if  the  moon  having  her  av- 
ctge  umbra  pass  between  the  earth  and  sun  at  her  aver- 
age distance  from  us,  the  umbra  would  not  reach  the 
earth  by  nearly  4,000  miles.  The  eclipse  in  this  case 
woidd  be  annular  and  not  total.  (See  annular  eclipses 
page  66). 

The  greatest  possible  diameter  of  the  moon's  umbra 
as  it  falls  upon  the  earth  is  about  175  miles,  and  this  can 
be  only  when  the  moon  is  at  her  greatest  distance  from 
the  sun  and  at  her  least  possible  distance  from  the  earth. 


62  LUNAR  TELLURIAN  MANUAL. 

Eclipses  are  known  as  solar  and  lunar,  and  as  the  terms 
indicate,  they  are  of  the  sun  and  moon. 


Lunar  Eclipses  may  be  -j 


or 


Lunar  Eclipses. 

If  the  moon  revolved  around  the  earth  in  the  plane  of 
the  ecliptic  she  would  pass  through  the  earth's  shadow 
and  be  eclipsed  at  every  full  moon,  and  would  throw  her 
own  shadow  upon  the  earth  at  every  new  moon.  Her 
orbit  is,  however,  inclined  to  the  ecliptic,  as  shown  by 
plate  E  on  the  globe.  That  she  may  pass  through  the 
earth's  shadow  and  be  eclipsed,  the  moon  must,  when 
full,  be  at  or  near  her  node,  otherwise  she  will  pass  above 
or  below  the  earth's  shadow.  It  is  not  necessary  that 
the  moon  be  exactly  at  her  node  to  strike  the  earth's 
shadow,  for,  if  within  10  ^degrees  either  before  or  after 
the  node,  she  will  pass  into  the  earth's  shadow  and  be 
wholly  or  partially  eclipsed,  according  to  her  nearness 
to  or  distance  from  the  node  when  she  "  fulls."  This 
distance,  10^  degrees  either  way  from  the  node,  is  called 
the  "  lunar  ecliptic  limits."  Thus  we  see,  that  at  either 
node  there  is  a  lunar  eclipse  limit  of  21  degrees  ;  includ 
ing  both  nodes,  42  degrees,  within  which  limits  all  lunar 
eclipses  must  occur. 

Move  the  arm  IX  of  the  globe  forward,,  until  the  moon 
ball  is  brought  to  "  full,"  as  shown  in  cut  No.  2  ;  loosen 
the  screw  holding  plate  E,  and  turn  the  plate  until  the 
gear-wheel  that  drives  the  moon  ball  rests  upon  the 
lower  part  of  the  plate,  as  shown  in  cut  ;  tighten  the 


LUNAR  TELLURIAN  MANUAL.  63 

screw,  ask  the  pupils  to  observe,  that  now  the  full  moon 
is  below  the  ecliptic  (the  line  J,  as  marked  upon  the 
globe),  and  that  the  shadow  of  the  earth  will  pass  above 
the  moon,  and  no  eclipse  will  occur. 

IJ^33//  is  important  that  the  pupils  remember,  that 
while  the  relative  sizes  of  the  earth,  sun  and  moon  are 
shown,  it  is  impossible  to  show  their  relative  distances. 
If  we  were  to  do  this,  the  globe  should  be  placed  about 
.a  mile  and  a  half  from  the  arc  S  and  the  moon  ball 
placed  about  20  feet  from  the  globe,  and  if  placed  at  these 
distances,  the  moon  ball  must  be  at  or  very  near  the 
globe's  ecliptic  when  full,  in  order  to  fall  within  the 
shadow  ;  a  little  variation  above  or  below  would  cause 
.the  moon  ball  to  miss  the  globe's  shadow  altogether. 

If  full  moon  occurs  when  the  moon  is  a  few  degrees 
(say  10  degrees)  before  she  reaches  her  ascending  node, 
she  will  pass  through  the  lower  portion  of  the  earth's- 
shadow,  thus  covering  the  upper  part  of  the  moon's  sur- 
face with  shadow,  giving  a  partial  eclipse  of  the  moon. 
Should  full  moon  occur  when  the  moon  is  10  degrees 
past  her  ascending  node,  her  lower  limb  or  edge  would 
be  eclipsed  by  the  higher  portion  of  the  earth's  shadow. 
Revolve  the  plate  E  one-half  way  around,  and  ask  the 
pupils  to  observe  that  now  the  moon  ball  is  above  the 
ecliptic  J,  and  that  the  shadow  must  fall  below  it.  If  full 
moon  occurs  when  the  moon  is  at  or  very  near  her  node, 
the  entire  moon  will  pass  through  the  earth's  shadow 
and  the  eclipse  will  be  total.  Such  an  eclipse  occurred 
.about  midnight  June  11,  1881. 

Solar  Eclipses. 

There  are  but  two  celestial  objects  that  can  ever  come 


64  LUNAR  TELLURIAN  MANUAL. 

between  us  and  the  sun  of  sufficient  size  to  cut  off  from 
us  the  solar  light.  These  two  are  the  moon  and  Venus. 
The  passage  of  the  planet  Venus  across  the  sun's  face, 
is  usually  called  a  transit  of  Venus.  The  last  transit  of 
Venus  occurred  Dec.  9,  1874.  The  next  will  take  place 
Dec.  6,  1882,  after  which  no  transit  will  occur  until  June 
8,  2004. 

There  are  three  classes  of  solar  eclipses,  viz. :  total, 
partial,  and  annular.  Let  us  treat  them  in  their  order. 

All  eclipses  of  the  sun,  caused  by  the  passage  of  the 
moon  between  us  and  the  sun,  must  occur  at  new  moon. 
Now,  if  new  moon  occur  while  she  is  in  the  vicinity  of 
her  node,  an  eclipse  of  some  kind  must  occur.  If  she  is 
at  or  very  near  her  node,  she  will  pass  across  the  sun's 
face  centrally,  or  very  nearly  so  ;  and  if  at  this  time  she 
happens  to  be  near  enough  to  us,  her  umbra  will  reach 
some  portion  of  the  earth's  surface,  and  to  that  region 
the  eclipse  will  be  total.  On  page  61  we  learned  that 
the  greatest  possible  diameter  of  the  moon's  umbra  at 
the  earth  is  175  miles;  the  usual  region  of  totality  is  very 
much  less.  Thus  we  see  why  total  eclipses  of  the  sun 
are  visible  to  so  small  portions  of  the  earth's  surface, 
while  a  lunar  eclipse  may  be  seen  from  any  part  of  an 
entire  hemisphere.  The  duration  of  solar  eclipses  is 
very  much  less  than  lunar.  The  length  of  totality  in  a 
solar  eclipse  cannot  exceed  6  or  7  minutes,  and  is  usually 
very  much  less,  while  the  moon  may  remain  totally 
eclipsed  for  nearly  two  hours.  The  apparent  size  of  the 
sun  and  moon  are  very  nearly  the  same,  and  it  requires 
the  entire  body  of  the  moon  to  hide  the  sun's  disc  and 
eclipse  him  wholly  ;  sometimes  she  is  not  able  to  do  even 
this,  as  we  shall  shortly  see. 


*  LUNAR  TELLURIAN  MANUAL.  65 

If  an  observer  were  stationed  on  the  moon  during  a 
total  lunar  eclipse,  he  would,  from  his  position,  see  a 
total  solar  eclipse.  To  him  the  apparent  size  of  the 
earth  and  sun  would  vary  greatly,  the  former  appearing 
between  thirteen  and  fourteen  times  larger  than  the  lat- 
ter. The  observer  so  stationed  could  not  have  an  eclipse 
of  the  earth,  as  the  largest  shadow  his  little  orb  could 
cast  upon  us  would  not  be  half  as  large  as  the  State  of 
Illinois,  and  to  him  it  would  appear  like  a  mere  speck 
floating  across  the  face  of  the  earth. 

Outside  of  the  field  of  totality  in  a  solar  eclipse  the 
eclipse  must  be  partial  when  it  is  seen  at  all.  Suppose 
the  city  of  St.  Louis  to  be  near  the  center  of  the  field  of 
totality  of  a  solar  eclipse.  At  the  moment  of  totality  in 
St.  Louis  an  observer  in  St.  Paul  would  see  the  moon  as 
below  the  sun,  and  in  the  passage  by,  his  face  would  ob- 
scure only  the  lower  portion  of  it  ;  to  him  the  eclipse  is 
partial.  An  observer  at  New  Orleans  would  see  the 
moon  passing  rather  above,  hiding  only  his  upper  limb  or 
edge,  while  a  person  in  South  America  could  not  see  the 
eclipse  at  all. 

Move  the  arm  IX  forward  until  the  moon  ball  is 
brought  to  new  moon,  as  in  cut  No.  1.  Move  the  plate  E 
until  its  highest  point  supports  the  moon  ball,  and  ask 
the  pupils  to  observe  that,  now  the  moon  is  above  the 
ecliptic  J,  and  the  shadow  of  the  moon  must  fall  above 
and  not  upon  the  earth  ;  were  they  placed  at  their  proper 
distance  (20  feet).  Move  the  plate  E  until  the  moon  ball 
falls  into  the  plane  of  the  ecliptic,  and  ask  the  pupils  to 
observe,  that  the  shadow  of  the  moon  in  this  position 
must  fall  upon  the  earth. 


66  LUNAR  TELLURIAN  MANUAL. 

On  page  61  we  find  the  average  length  of  the  moon's 
umbra  is  236,000  miles,  and  her  average  distance  from 
the  earth  240,000  miles,  so,  should  the  moon  pass  across 
the  sun's  face  when  so  situated  the  umbra  would  not 
reach  the  earth  by  some  4,000  miles.  The  apparent  size 
of  the  moon  is  now  smaller  than  the  sun,  and  she  would 
in  this  position  be  unable  to  hide  his  entire  face  from  us, 
and  when  passing  by  his  center,  a  ring  or  fringe  of  light 
would  be  seen  all  around  the  moon.  An  eclipse  of  this 
kind  is  called  annular.  The  word  annular  means  like  a 
ring  or  ring  shaped,  referring  to  the  ring  or  fringe  of 
light  seen  around  the  moon.  Thus  we  see  that  the  moon 
must  be  nearer  the  earth  than  her  average  distance,  or 
that  the  sun  must  be  at  a  greater  than  his  average  distance 
to  make  it  possible  for  the  moon  to  hide  his  entire  face 
and  to  produce  a  total  eclipse  of  the  sun. 

Move  the  arm  IX  forward,  and  ask  the  pupils  to  ob- 
serve, that  the  apparatus  shows  the  moon  sometimes 
nearer  the  earth  than  at  others. 

* 

It  is  not  necessary  that  new  moon  occur  exactly  at  the 
moon's  nodes  to  give  an  eclipse  of  the  sun  ;  if  within 
16  y2  degrees  of  it  either  way,  she  will  eclipse  him.  Thus 
we  see  the  "  solar  ecliptic  limit  "  is  33  degrees  at  either 
node  or,  in  all,  66  degrees  for  both  nodes,  and  within  this 
limit  must  all  solar  eclipses  occur. 

Why  more  Solar  than  Lunar  Eclipses. 

On  page  62  we  see  the  moon  must  be  within  10  J^  de- 
grees (either  before  or  after)  of  her  node  at  Full  Moon 
to  enter  the  earth  shadow,  consequently  her  Lunar  Eclip- 
tic limit  is  10^  -f  10 5^  =21  degrees  at  either  node,  or 
a  total  of  42  degrees  of  her  orbit  wherein  lunar  eclipses 


LUNAR  TELLURIAN  MANUAL.  67 

may  occur.  In  the  last  section  we  see  the  solar  ecliptic 
limit  is  33  degrees  at  either  node,  or  a  total  of  66  degrees 
in  which  solar  eclipses  may  occur.  Then  it  follows  that 
the  proportion  of  solar  to  lunar  eclipses  is  the  same  as 
66  bears  to  42  or  as  11  to  7.  . 

Season  of  Eclipses. 

We  have  already  learned  (page  55)  that  the  time  from 
one  node  to  another  is  173  days.  If  a  new  moon  occurs 
near  ascending  node  and  eclipse  the  sun,  in  173  days  fol 
lowing,  full  moon  will  occur  near  the  descending  node 
and  she  will  pass  into  the  earth's  shadow  and  be  eclipsed. 
Last  year,  1881,  the  moon's  nodes  occurred  about  June 
11,  and  December  1.  This  year,  1882,  they  occur  about 
19  days  earlier,  or  about  May  22,  and  November  11,  and 
so  continue  from  year  to  year,  owing  to  the  falling  back 
of  the  moon's  nodes.  (See  page  53.) 

The  Solar  Ecliptic  limit  33  degrees,  is  equal  in  time 
to  36  days.  So  an  eclipse  of  the  sun  may  occur  18  days 
before  or  18  days  after  the  moon's  node,  which,  the  past 
year  1881,  extended  from  May  23  to  June  29  ;  while  the 
solar  ecliptic  limit  for  the  opposite  node  embraces  the 
time  from  November  12  to  December  18. 

The  Lunar  Ecliptic  limit  21V  degrees,  is  equal  to  23 
days,  thus  an  eclipse  of  the  moon  may  take  place  at  any 
full  moon  occurring  11  yz  days  before  or  after  the  node. 
Thus  the  Lunar  Ecliptic  season  is  from  may  30  to  June 
22,  and  from  November  19  to  December  12,  of  the  year 
1881. 

The  Period  of  Eclipses. 

By  referring  to  the  subject  of  the  moon's  nodes  (page 


68  LUNAR  TELLURIAN  MANUAL. 

54)  we  find  the  nodes  are  not  fixed,  but  have  a  retrograde 
movement  on  the  ecliptic,  nearly  20  degrees  every  year, 
or  at  a  rate  that  will  carry  them  clear  around  the  ecliptic 
in  about  18  years,  5  months.  If  we  mark  carefully  the 
position  of  the  nodes  on  .the  ecliptic  now,  and  note  the 
eclipses  that  occur  for  18  years,  5  months,  and  record  the 
result,  and  observe  the  phenomena  for  a  like  period  fol- 
lowing, we  shall  find  the  eclipses  for  the  latter  period 
almost  identical  with  those  of  the  first.  Knowing  this  the 
astronomers  are  able  to  foretell  eclipses  to  the  very  day 
and  hour  a  hundred  years  in  advance  of  their  occurrence  ! 
These  periods  are  called  the  Saros  or  Period  of  Eclipse. 

The  Precession  of  the  Equinoxes. 

The  precession  of  the  equinoxes  is  due  to  a  gyratory 
movement  of  the  earth's  axis  revolving  the  poles  of  the 
equator  around  the  poles  of  the  ecliptic.  As  the  equa- 
tor or  equinoctial  and  the  ecliptic  cut  each  other  at  an 
angle  of  23^  degrees,  so  must  their  axis  bisect.  Upon 
the  globe  is  marked  the  equator  and  ecliptic.  The  poles 
of  the  equator  are  the  ends  of  the  axis  of  the  globe,  and 
the  poles  of  the  ecliptic  the  points  where  a  vertical  line 
drawn  through  the  center  of  the  globe  would  cut  its  sur- 
face. This  gyratory  movement  of  the  earth's  axis  is  very 
slow,  requiring  about  25,800  years  to  complete  one  revo- 
lution. The  effect  of  the  movement  is  to  carry* the 
equinoctial  and  solstitial  points  backward,  slowly,  around 
the  ecliptic  from  east  to  west.  The  value  of  this  move- 
ment annually  is  50.1  seconds  of  arc.  The  earth's  orbit, 
like  all  circles,  is  divided  into  360  degrees,  these  degrees 
subdivided  into  minutes  and  •  the  minutes  into  seconds. 


LUNAR  TELLURIAN  MANUAL.  69 

The  exact  solar  year*  is  the  time  required  by  the  earth 
to  travel  360  degrees  of  its  orbit,  less  50.1  seconds,  or 
359  deg.,  59  min.,  9.9  sec.  To  illustrate  upon  the  globe 
the  precession,  or  more  properly  the  recession  of  the 
equinoxes,  proceed  as  follows  : 

1.  Arrange  the  globe  as  shown  in  cut  II,  page  9  ;  ro- 
tate the  globe  upon   its   axis  until  the   ecliptic  upon  the 
globe  lies  in  a  horizontal  plane. 

2.  Move  the  arm  O  slowly  to  the  left,  completing  a 
circle  around  the  standard  P,  and  observe  that  as  this  is 
done  the  poles  of  the  equator  describe  circles  around  the 
poles  of  the  ecliptic  (the  north  pole  of  the  ecliptic  on  the 
globe  being  where  the  90th  meridian  east  crosses  the  arc- 
tic circle).     In   like  manner  the  poles  of  the  earth  de- 
scribe circles  around  the  poles  of  the  ecliptic  once  every 
25,800  years,  as  before  stated. 

3.  Adjust  the  globe  for  the  calendar  ;  move  the  globe 
slowly  forward  to  its  orbit,  and  observe  that  the  pointer 
,X  traces  the  ecliptic,  crossing  the  equator,  giving  equi- 
noxes about  March  20  and  September  23. 

4.  Move   the  arm  O  a  part  of  the    way   around    the 
standard  P,  as  in  2  above,  say  one-half  of  an  inch;  move 
it  forward  to  its  orbit,  and  observe  that  the  equinoxes  do 
not  occur  at  the  same  points  in  the  orbit  as  in  the  former 
instance,  but  earlier.     Repeat  the  operation,  moving  the 


*Quite  frequently  called  the  Tropical  Year.  There  are  generally  reckoned 
three  years,  i.  Sidereal  Year,  as  the  time  required  by  the  earth  to  make  one 
complete  orbital  movement,  or  365  days,  6  hours,  9  minutes,  9  seconds.  2.  The 
Solar  or  Tropical  Year,  as  the  time  required  for  the  sun's  vertical  ray  to  pass 
from  tropic  to  tropic  and  return,  or  365  days,  5  hours,  48  minutes,  46  seconds. 
3.  The  Civil  Year  of  365  and  366  days,  according:  as  the  year  is  a  common  or 
leap  year. 


70  LUNAR  TELLURIAN  MANUAL. 

arm  O  little  by  little,  and  observe  the  equinoctial  points 
falling  back  in  the  orbit  as  the  arm  O  is  moved. 

5.  The  vernal  equinox  occurs  as  the  sun  enters  the 
first  degree  of  the  sign  Aries  of  the  Zodiac.  If  these 
signs  were  fixed  as  regards  the  orbit,  manifestly  the  next 
succeeding  vernal  equinox  would  occur  50  1  seconds 
before  the  sign  Aries  were  reached,  and  so  continue  to 
fall  back  in  the  signs  from  year  to  year.  The  signs,  how- 
ever, are  shifted  to  agree  with  the  falling  back  of  the 
equinoxes  ;  thus  the  equinoxes  will  always  occur  in 
the  same  degree  and  sign  as  now.  The  signs,  how- 
ever, do  not  agree  with  the  constellations  from  which 
they  derive  their  names. 

Equation  of  Time. 

Sidereal,  Solar  and  Mean  Time. 

Time  is  a  measurement  of  duration.  One  of  the  first 
objects  of  astronomical  study  was  to  find  a  standard  for 
the  measurement  of  Duration.  For  this  purpose  the  ap- 
parent diurnal  revolution  of  the  sun  marked  the  begin- 
nings and  endings  of  the  standard  days  ;  while  this  did 
not  mark  duration  into  uniform  periods  of  time,  it  was 
found  to  be  sufficiently  accurate  for  the  civil,  and  the 
crude  astronomical  uses  of  the  earlier  days.  The  sun-dial 
served  to  mark  the  subdivisions  of  the  day  ;  but  as  the 
dial  was  useless  in  the  night  time  or  in  cloudy  weather, 
a  more  reliable  indicator  was  sought  in  mechanical  de- 
vices, similar  to  our  clocks  and  watches.  The  makers 
of  these  were  sorely  perplexed  because  they  could  not 
make  their  machines  "  agree  with  the  sun  "  for  any  con- 
siderable time  ;  because  of  this,  we  are  told,  the  makers 
suffered  persecution,  and  their  machines  fell  into  disre- 


LUNAR  TELLURIAN  MANUAL.  71 

pute,  and  were  little  used  ;  and  where  used  at  all,  they 
merely  supplemented  the  sun-dial,  by  which  they  were 
"  regulated  "  from  time  to  time. 

It  was  soon  discovered  that  the  sun  days  were  not  of 
uniform  length,  and  that  the  machines  were  the  better 
time-keepers.  The  causes  of  this  variation  will  be  ex- 
plained before  we  leave  the  subject. 

The  Sidereal  Day  is  the  period  that  elapses  between 
two  successive  transits  of  any  fixed  star  ;  this  period  is 
unvarying.  The  length  of  the  sidereal  day  is  24  sidereal 
hours,  or  23  hours,  56  minutes,  4  seconds  of  "mean  time." 

The  Solar  Day  is  the  period  tkat  elapses  between  two 
successive  transits  of  the  sun  ;  this  period  varies  in  length, 
being  sometimes  more  and  sometimes  less  than  24  mean 
time  hours.  Thus  it  is  that  the  clock  and  sun  do  not 
agree. 

The  Mean  Day  or  the  Mean  Solar  Day  is  the  aver- 
age length  of  all  the  solar  days  of  the  year,  and  is  of 
course  unvarying  in  length,  and  is  the  standard  civil  day 
which  our  clocks  and  watches  are  made  to  keep.  The 
mean  day  is  3  minutes  56  seconds  longer  than  the  sid- 
ereal day. 

The  varying  lengths  of  the  solar  days  depend  upon 
two  causes  : 

1.  The  unequal  velocity  at  'which  the  earth  travels  in 
its  orbit. 

2.  The  inclination  of  the  equator  to  the  ecliptic. 


72  LUNAR  TELLURIAN  MANUAL. 

1.  To  Illustrate  that  the  Unequal  Velocity  of  the 
Earth  in  its  Orbit  is  a  Cause  of  the  Existing 
Variation  of  the  Lengths  of  the  Solar  Days. 

Arrange  the  globe  as  shown  in  cut  2,  page  36,  and 
proceed  as  follows  : 

Bring  the  calendar  index  to  the  21st  of  June  ;  rotate 
the  globe  upon  its  axis  until  the  prime  meridian  is  under 
the  pointer  L  ;  extend  the  pointer  L  until  it  is  within  1-16 
of  an  inch  of  the  globe.  Move  the  globe  forward  in  its 
orbit  an  entire  revolution,  and  observe  that  the  pointer  L 
is  by  this  movement  carried  from  'west  to  east  across  the 
meridians  at  a  rate  that  will  carry  it  clear  around — 360 
degrees — in  one  year  of  365^  days  (about),  or  a  trifle 
less  than  a  degree  a  day,  on  the  average.  This  distance 
is  equal  in  time  to  3  minutes  56  seconds. 

Rotate  the  globe  upon  its  axis  from  west  to  east,  and 
observe  that  this  movement  carries  the  pointer  L  across 
the  meridians  from  east  to  west  at  a  rate  that  will  carry 
it  clear  around  in  one  day  ;  so  it  follows  that  while  the 
daily  rotation  is  carrying  the  sun's  vertical  ray  360  de- 
grees from  east  to  west,  the  forward  movement  of  the 
earth  in  its  orbit  is  carrying  it  back  nearly  a  degree 
(about  59  minutes  of  distance),  from  west  to  east.  There- 
fore, the  earth  must  turn  more  than  once  upon  its  axis  to 
complete  a  solar  day.  This  little  "  more  "  in  a  year 
amounts  to  360  degrees,  a  revolution.  So,  the  truth  is 
apparent  that  the  earth  must  turn  366  times  upon  its  axis 
to  complete  365  solar  days  ;  or  366  sidereal  days  are 
equal  to  365  solar  days. 

If  the  movement  of  the  earth  in  her  orbit  were  uni- 
form day  to  day  throughout  the  year,  the  variation 
would  be  uniform^  and  the  solar  days  would  be  of  equal 
length. 


LUNAR  TELLURIAN  MANUAL.  73 

As  the  orbital  movement  of  the  earth  is  not  uniform,* 
and  the  daily  revolution  is  uniform,  a  variation  in  the 
lengths  of  the  solar  days  must  follow. 

2.  To  Illustrate  that  the  Inclination  of  the  Equator 
to  the  Ecliptic  is  a  Cause  of  the  Existing  Varia- 
tion in  the  Lengths  of  the  Solar  Days. 

Arrange  the  globe  as  shown  in  cut  2,  page  36.  Bring 
the  calendar  index  to  the  20th  of  March,  rotate  the  globe 
upon  its  axis  until  the  ecliptic  lies  in  a  horizontal  plane. 
Ask  the  pupils  to  observe  :  That  the  equator  and  the 
ecliptic  are  both  great  circles,  and  that  a  degree  of  one 
is  equal  to  a  degree  of  the  other.  That  the  earth  rotates 
in  the  direction  of  the  plane  of  the  equator.  The  verti- 
cal sun  travels  on  the  ecliptic,  a,  Move  the  globe  for- 
ward in  its  orbit  a  few  degrees,  and  observe  that  this 
movement  has  carried  the  pointer  L  so  many  degrees 
east  and  north  on  the  ecliptic,  but  has  not  changed  its 
longitude  to  so  great  an  amount  as  would  have  been  the 
case  if  all  the  movement  had  been  directly  east,  or  with 
the  rotation,  instead  of  being  at  an  angle  to  it.  Briftg 
the  calendar  index  to  March  20,  rotate  the  globe  until  the 
prime  meridian  is  directly  under  the  pointer  L  ;  move 
the  globe  forward  in  the  orbit  until  the  pointer  L,  tracing 
the  ecliptic,  is  brought  to  the  10th  parallel.  Observe 
that  the  orbit  movement  has  carried  the  sun  east  and 
north  ;  rotate  the  globe  slowly  on  its  axis  from  west  to 

*The  velocity  at  which  a  planet  travels  depends  upon  its  distance  from  the 
sun.  The  nearer  to  the  sun  the  greater  is  his  attraction,  and  the  greater  the 
velocity  must  be  to  keep  the  pianet  from  going-  to  him.  The  orbit  of  the  earth 
is  an  ellipse,  and  the  sun  is  situated  in  one  of  the  foci.  In  obedience  to  this 
law  the  earth  travels  faster  when  near  perihelion  (Dec.,  Jan.,  Feb.,)  than  when 
near  aphelion  (June,  July,  Aug.)  Other  things  being  equal,  it  follows  that  the 
solar  days  are  longer  in  Winter  than  in  Summer. 


74  LUNAR  TELLURIAN  MANUAL. 

east,  and  observe  this  movement  carries  the  pointer  L 
back  to  the  prime  meridian  not  on  the  line  of  the  ecliptic, 
but  following  the  parallel.  Thus  the  orbital  movement 
carries  the  sun  forward  on  an  angle,  and  the  daily  rota- 
tion brings  it  back  on  a  straight  line  describing  two  lines 
of  a  triangle,  of  which  the  ecliptic  is  the  hypothenuse,  a 
parallel  of  latitude  and  the  prime  meridian  being  the 
other  two  sides. 

Owing  to  the  angling  movement  about  1-12  of  the 
displacement  is  lost,  thereby  shortening  the  solar  day  1-12 
of  3  minutes  56  seconds  (the  average  displacement),  or 
about  20  seconds,  b.  Move  the  globe  forward  to  the 
position  it  occupies  about  the  1st  of  June,  and  observe 
that  from  this  time  until  about  August  1st  the  movement 
of  the  sun  on  the  ecliptic  is  nearer  in  the  direction  of 
the  rotation  than  in  March.  Also,  that  a  degree  on  the 
ecliptic  is  greater  than  a  degree  upon  the  parallels  to 
which  the  sun  is,  at  this  season,  vertical,  and  the  daily 
rotation  is  slower.*  Owing  to  this,  about  1-12  of  this 
displacement  is  gained,  thereby  lengthening  the  solar 
day  1-12  of  3  minutes  56  seconds,  or  about  20  seconds. 

The  Tides. 

The  Subjoined  Explanation  of  the  Mathematics 
of  the  Tidal  Movements  is  by  Prof.  E.  Colbert, 
the  well  known  Astronomer  of  the  Chicago 
Tribune. 

The  waters  of  the  ocean  are  in  ceaseless  motion,  rising 
and  falling  twice  in  each  lunar  day,  or  about  every  25 

*The  surface  of  the  earth  at  the  equator  travels  faster  in  its  diurnal  motion 
than  the  surface  at  the  the  tropics,  being  nearly  250  miles  farther  from  the 
tarth's  axis 


LUNAR  TELLURIAN  MANUAL.  75 

hours.  The  rising  of  the  waters  is  called  the  flow  or 
Hood  tide,  and  the  falling  of  the  same  the  ebb  tide.  The 
height  to  which  the  waters  rise  through  a  number  of 
succeeding  tides  is  not  uniform,  as  will  be  explained  here- 
after. The  greater  are  called  Spring,  and  the  lesser 
Neap  tides.  The  waters  act  in  obedience  to  that  one 
universal  law  of  gravity,  which  may  be  expressed  as 
follows  ; 

All  bodies  attract  all  other  bodies  throughout  space 
directly  in  proportion  to  the  quantity  of  matter  they  con- 
tain, and  inversely  as  the  squares  of  the  distance  be- 
tween them.  We  may  further  add  that  the  force  of  at- 
traction is  exerted  in  the  direction  of  a  straight  line  join- 
ing their  centers  of  gravity.  The  subjoined  example 
will  explain  the  application  of  this  law. 

Let  two  bodies  be  placed  ten  feet  apart,  the  weight  of 
A  to  be  2  tons  and  that  of  B  1  ton  ;  their  attraction  for 
each  other  is  directly  as  their  matter,  or  as  2  is  to  1. 

Let  10  equal  the  power  of  attraction  of  A  for  B  and 
5  equal  the  power  of  attraction  of  B  for  A.  Separate 
the  bodies  20  feet  ;  they  now  attract  each  other  in  the 
same  ratio,  i.  e.  2  to  l,but  with  diminished  power.  The 
square  of  the  first  distance  (10  feet)  is  10  X  10  =  100. 
The  square  of  the  second  distance  (20  feet)  is  20  X  20 
=  400.  According  to  the  law  above  given  the  attract- 
ing power  of  A  and  B  in  the  two  positions  is  inversely, 
as  100  is  to  400,  or  directly,  as  400  is  to  100,  or  as  4  to  1 
in  the  respective  distances  of  10  and  20  feet.  Thus  we 
see  that  at  10  feet  the  attractive  power  is  four  times 
greater  than  it  is  at  20  feet.  If,  as  stated,  the  attracting 
power  of  A  for  B  at  10  feet  is  2,  at  20  feet  it  is  2  -f-  4 


76  LUNAR  TELLURIAN  MANUAL. 

=  f  or  £.     For  B  at  10  feet  the   power  is  1,  at  20  feet  it 
is  1-4  =^. 

The  average  tide  producing  influence  of  the  moon  as 
compared  with  that  of  the  sun  is  nearly  as  2^  is  to  1. 
The  tides  in  open  ocean  do  not  rise  to  exceed  5^  feet, 
while  in  the  breakers  of  the  tidal  wave  as  it  reaches  a 
continent  the  water  rises  very  much  higher.  In  the 
Bay  of  Fundy,  the  waters  sometimes  rise  nearly  100  feet. 
At  Boston  the  tide  is  usually^bout  14  feet. 

The  tides  of  our  oceans  are  due  to  the  difference  be- 
tween the  attractive  force  exerted  by  the  moon  and  sun  ; 
on  the  earth  as  a  whole,  and  on  the  waters  at  her  sur- 
face. The  following  explanation  of  the  theory  of  the 
tides  only  applies  strictly  to  such  parts  of  the  ocean  sur- 
face as  are  not  near  to  considerable  masses  of  land  sur- 
face. The  retardation  of  the  tidal  wave  in  moving 
through  shallow  water,  with  the  changes  in  its  direction, 
speed,  and  volume,  caused  by  continents  and  islands,  are 
matters  which  belong  more  to  physical  geography  than 
to  astronomy.  It  may  be  well  to  note,  however,  that 
even  in  the  deep  waters  of  the  mid  Pacific,  the  tidal  wave 
is  retarded  by  the  same  cause  that  makes  it  travel  behind 
the  moon  instead  of  keeping  directly  under  her  ; — fric- 
tion. The  tide  wave  that^gathers  on  the  eastern  side  of 
the  Pacific  Ocean  follows  about  two  hours  behind  the 
moon,  and  occupies  about  40  hours  in  passing  round  to 
our  Atlantic  coast  ; — less  than  a  cercumference  of  the 
globe. 

Let  M  represent  the  position  of  the  moon  ;  A  D  the 
earth,  and  E  its  center.  If  we  take  E  A,  or  E  D,  the 


LUNAR  TELLURIAN  MANUAL.  77 

earth's  radius,  as  unity,  then,  for   the    least  possible  dis- 
tance  of  the   moon  ;  MA  =  55  ;  ME  =  56  ;  and  MD 


Let  m  denote  the  measure  of  the  moon's  attractive 
force  at  the  unit  of  distance  ;  it  equals  about  375,800 
feet.  Then  the  disturbing  force  on  the  water  at  A  will 
be  measured  by 

m  m 

(55)~2  —  (56)*  5=         4-40  feet- 

Similarly  ;  the  moon's  disturbing  force  on  the  water 
at  D  is  measured  by  : 

m  m 

(56f  —  (5T)5  ;  =         4-17  feet. 

2  m 

We  may  also  calculate  that  pgjja  =  4-28  ;  which  is 
the  mean  of  the  above  results,  and  is  the  mean  tide  due 
to  the  moon  acting  at  her  least  possible  distance.  The 
calculation  gives  0*12  more  for  the  tide  under  the  moon, 
and  0-11  less  for  the  opposite  tide.  The  differences  are 
really  much  less  than  this  ;  owing  to  the  fact  that  the 
crests  of  the  two  tides  are  at  a  and  d  instead  of  on  the 
line  AD.  In  the  open  ocean  they  lag  about  43  degrees 
behind  the  place  of  the  moon,  and  its  opposite  ;  and  are 
still  more  retarded  when  they  meet  with  land  masses. 


78  LUNAR  TELLURIAN  MANUAL. 

The  greatest  possible  distance  of  the  moon  from  the 
earth's  center  is  about  64  times  the  earth's  equatorial 
radius.  Calculating  as  before,  we  have  : 

m  m 

Direct  tide          =  —  —         2'94  feet. 


m  m 

Opposite  tide      =  (64)2  —  ^5^2  ;  =         2'80  feet. 

2  m 
Mean  tide          —  (54)3  ;  =         2-87  feet. 

In  this  case,  as  in  the  other,  the  tide  equals  %m  divided 
by  the  cube  of  the  relative  distance  from  the 
earth's  center,  plus  and  minus  a  small  quantity.  All 
perturbations  due  to  the  force  of  attraction  vary  inversely 
as  the  cube  of  the  relative  distance,  plus  or  minus  a 
correction  which  decreases  with  an  increase  in  the  rela- 
tive distance. 

The  least  and  greatest  distances  of  the  moon  in  her 
{average)  orbit,  are  about  57  and  63^.  These  corre- 
spond to  4*06  feet,  and  2-94  feet  respectively.  Half  the 
sum  of  these  two  is  3*5  feet,  which  is  about  the  average 
height  of  crest  of  the  lunar  tide  wave  in  the  open  ocean. 

The  sun  also  causes  a  tide.  Our  distance  from  him 
when  in  Perihelion  is  23,020,  and  when  in  "Aphelion 
23,805  times  the  earth's  equatorial  radius.  The  value  of 
m^  for  these  assumptions  of  distance  of  the  sun,  is 
8,900,000,000,000,  nearly.  The  resulting  values  of  the 
solar  tide  are  1-44  and  1-30  feet  ;  average  1'37  feet. 

The  lunar  and  the  solar  tides  move  after  the  place  of 
their  respective  causes  in  the  heavens,  as  the  earth  turns 
round  under  them.  At  the  times  of  New  and  Full 
Moon  the  two  forces  coincide,  and  the  united  tide  is  equal 


LUNAR  TELLURIAN  MANUAL.  79 

in  magnitude  to  the  sum  of  the  two  :  being  (4*06  -f- 1'44) 
=5'50  feet,  when  the  earth  is  nearest  to  sun  and  moon  ; 
and  (2-94  -f  1-30)  =  4-24  feet,  when  both  are  at  their 
greatest  distance.  When  the  moon  is  in  her  first  or  third 
quarters,  the  depression  caused  by  the  sun  coincides  with 
the  elevation  caused  by  the  moon  ;  and  the  tide  varies 
from  (4-06  —  1-30)  =  2-76  feet,  when  the  moon  is  in 
perigee  and  the  earth  in  'aphelion,  to  (2-94  —  1-44)  =1'5 
feet,  when  the  moon  is  in  apogee  and  the  earth  in  peri- 
helion. 

The  crest  of  each  direct  tide  is  theoretically  40  to  45 
degrees  or  about  2  hours  50  minutes,  late  on  the  parallel 
of  latitude  corresponding  to  the  declination  of  body  caus- 
ing the  tide.  That  is,  if  the  moon  be  in  20  degrees  north 
declination,  the  direct  lunar  tide  will  be  in  20  degrees  of 
north  latitude.  The  crest  of  the  opposite  tide  is,  simi- 
larly, moving  in  latitude  opposite  to  the  declination.  Let 
u  denote  the  angular  distance  of  any  point  on  the  earth's 
surface  from  the  crest  of  the  lunar  wave  at  a  given  mo- 
ment ;  iv  its  angular  distance  from  the  crest  of  the  solar 
wave  at  the  same  instant  ;  ^4,  the  height  of  the  lunar 
crest  ;  and  B,  the  height  of  the  solar  crest.  Then  the 
height  of  the  tide  at  the  designated  time  and  place,  will 
equal  : 

A.  cos.  (2  u]  +  B.  cos.  (2  -w)  : 

remembering  that  the  cosine  of  an  angle  greater  than 
90  degrees  and  less  than  270  degrees,  is  essentially 
negative. 


READ  THE 

OPINION  OF  CAPABLE  JUDGES  : 

"  HEADQUARTERS  ILLINOIS  TEACHERS'  ASSOCIATION, 
SPRINGFIELD,  DEC.  29,  1880. 

"  A.  H.  ANDREWS  &  Co., 

"  Gentlemen  : — Your  new  Lunar  Tellurian  Globe  is  a 

splendid   apparatus    for   class   use   in    illustrating    Mathematical 

Geography.     The  relationships  of  the  earth,  sun  and  moon  are 

well  and  clearly  shown.     The  Globe  has  more  merit  and  fewer 

defects  than  any  similar  apparatus  we  have  ever  seen.     It  is  a 

credit  to  the  inventor  and  manufacturers.     Yours  respectfully, 

"M.  L.  Seymour,  of  Normal  University,  Bloomington. 

"  E.  A.  Gastman,  Supt.  Schools,  and  President  Illinois  Teachers' 
Association. 

"  D.  S.  Wcntworth,  Principal   Cook   Co.  Normal  School,  Engle- 
wood,  111. 

"  Henry  L.  Boltwood,  Principal  Ottawa  Township  High  School- 
Ottawa,  111. 

"  M.  Andrews,  Supt.  City  Schools,  Galesburg,  111. 

"  Leslie  Lewis,  Supt.  Schools,  Hyde  Park,  111. 

"J.  Pike,  "  "        Jerseyville,  111. 

"  W.  H.  Williamson,  Prin.  Schools,  Havana,  111. 

"  R.  W.  Mathews,          "  "         Chester,  111. 

"  Geo.  Blount,  Supt.  Schools,  Macomb,  111. 


Letter  from  Prof.  E.  COLBERT,  Astronomer  of  the  Chicago 
Tribune. 

CHICAGO,  ILL.,  May,  2.  1881. 
A.  H.  ANDREWS  &  Co. 

Gentlemen: — I  have  carefully  examined  your  "  Lunar 
Tellurian  "  and  am  charmed  with  it.  The  apparatus  may  be  used 
to  illustrate  many  of  the  phenomena  that  are  due  to  the  move- 
ments of  the  earth  and  moon,  with  reference  to  the  sun;  and  con- 
veys a  much  clearer  idea  of  the  same  than  has  hitherto  been 
obtained  by  the  great  majority  of  those  who  have  essayed  to 
understand  them.  So  far  as  I  know,  it  is  unequaled. 
Very  respectfully, 

E.   COLBERT. 


The  Solar  System.* 

THE  SOLAR  SYSTEM,  as  known  to  us  through  the  discoveries  of  Copernicus , 
Kepler,  Newton  and  their  successors,  consists  of  the  Sun  as  a  central  body, 
around  which  revolve  the  major  and  minor  planets  with  their  satellites,  a  few 
periodic  comets,  and  an  unknown  number  of  meteor  swarms. 

The  bodies  of  the  system  may  be  classified,  as  follows  :  i.  The  SUN,  the 
center  of  our  portion  of  the  universe  or  the  solar  system.  2.  The  four  inner 
planets.  Mercury,  Venus,  Earth,  Mars.  3.  A  group  of  small  planets  called 
Asteroids  revolving  outside  of  the  orbit  of  Mars.  4.  A  group  of  four  outer 
placets,  ^Jupiter,  Saturn,  Uranut  and  Neptune.  5.  The  satellites  revolving 
about  their  primaries  the  planets.  6.  A  number  of  comets  and  meteor  swarms 
revolving  in  very  eccentric  orbits  about  the  sun .  The  8  planets  of  groups  2  and 
4  are  called  Major  planets  to  distinguish  them  from  the  200  or  more  Minor 
planets  of  group  3. 

The  relative  sizes  of  the  planets  if  viewed  from  an  equal  distance  from  all 
of  them  would  be  somewhat  as  follows  :  Jupiter,  \%  inches  in  diameter  ;  Sat- 
urn, i%  inches ;  Neptune,  9- 16  inches  ;  Uranus,  %  inch  ;  Earth  and  Venus  less 
than  %  inch ;  Mars  a  pin-head,  and  Mercury  a  little  more  than  a  point. 

The  relative  sizes  of  the  Sun  as  seen  from  the  different  planets  would  be 
somewhat  as  follows:  Frorri  Mercury  the  sun  would  appear  i^  inches  in 
diameter  ;  from  Venus,  %  inch  ;  from  Earth,  yz  inch  ;  Mars,  %  inch  ;  Jupiter, 
i-i6inch;  Saturn,  1-20  inch;  Uranus,  1-50  inch;  Neptune,  a  mere  point. 

If  we  represent  the  sun  by  a  gilded  globe,  2  feet  in  diameter,  we  must  show 
Vulcan  and  Mercury  by  mustard  seeds ;  Venus  by  a  pea,  Earth  by  another, 
Mars  by  half  that  size,  Asteroids  by  the  motes  in  a  sunbeam,  Jupiter  by  a 
small  orange,  Uranus  by  a  cherry,  and  Neptune  by  one  a  little  larger. 

The  relative  distances  of  the  planets  from  the  sun  may  be  represented 
approximately  by  the^e  figures  :  Mercury  4,  Venus  7,  Earth  10,  Mars  15,  Ceres 
(a  Minor  planet)  28,  Jupiter  52,  Saturn  95,  Uranus  192,  Neptune  300. 

THE  SUN. — The  distance  of  the  Sun  from  us  is  said  to  be  about  92%  million 
miles.  No  one  could  even  count  this  number  in  a  year's  time  !  The  diameter 
of  the  Sun  is  860,000  miles  ;  hence  his  radius  is  twice  the  mean  distance  of  the 
Moon  from  the  Earth.  The  Sun's  volume  is  1,300,000  times  that  of  the  Earth, 
and  his  mass  over  700  times  that  of  all  other  bodies,  including  Earth.  Hence, 
the  center  of  gravity  of  the  whole  system  is  very  little  outside  of  the  body  of  the 
Sun,  and  will  be  inside  of  it  when  Jupiter  and  Saturn  are  in  the  opposite  direc- 
tions. The  Earth  receives  less  than  one  two  billionth  part  of  the  solar  heat  or 
radiation  !  How  much  heat  then  is  lost  in  space  !  Hut  suppose  the  source  of 
our  heat  supply  to  b  j  gradually  diminished  for  some  cause,  how  fatal  the  con- 
sequence to  the  inhabitants  of  Earth  !  Among  the  theories  as  to  the  source  of 
heat  supply  in  the  Sun  is  this,  viz  :  that  there  is  a  constant  contraction  of  the 
solar  sphere.  Theory  indicates  that  in  five  millon  years  the'  Sun  will  be  reduced 
to  half  its  present  size.  His  density  is  about  one-fourth  that  of  the  Earth. 
Zollner  says  the  sun  revolves  on  its  axis  at  the  rate  of  660  miles  an  hour. 

MERCURY. — But  little  is  known  of  this  planet.  Being  so  near  the  sun  it  can 
be  seen  only  just  after  sunset  or  before  sunrise,  and  scarcely  ever  visible  without 
a  telescope  Mercury  and  Venus  have  much  in  common,  both  being  within  the 
orbit  of  the  Earth.  Mercury  is  about  36  million  miles  from  the  Sun.  His 
diameter  is  about  3,000  miles.  His  year 'is  about  88  of  our  days.  Axial  revolu- 
tion about  same  as  ours;  orbital  velocity,  1773  miles  a  minu'e. 

VENUS. — This  is  called  the  second  planet,  her  year  being  about  225  of  our 
days  ;  distance  from  sun,  66,750,000  miles  ;  diameter,  7,660  miles  ;  orbital  veloc- 
ity, 1,300  miles  a  minute.  Venu's  may  be  as  near  Earth  as  22,000,000  miles,  or 
as  far  as  160,000,000. 

EARTH. — This  is  the  third  planet  in  distance  from  the  Sun,  and  moves  in 
her  yearlv  orbit  69,000  miles  per  hour,  1,152  miles  per  minute,  or  19  miles  per 
second.  In  our  daily  revolution,  we,  of  course,  move  at  the  rate  of  about  1000 
miles  per  hour. 


*These  items  are  compiled  from  Newcomb  and  other  sources,  by  E.  N.  A. 


MOON. — The  Earth  being  larger  than  her  satellite,  we  can  see  more  than 
half  her  surface,  sav  58-100.  The  difference  in  heat  on  the  Moon  at  noon  and 
midnight,  is  500  degrees.  The  Moon  gives  us  only  1-618,000  as  much  light  as 
the  Sun.  The  sky  full  of  moons  woufd  not  give  us  daylight.  There  have  re- 
cently been  discovered  some  signs  of  atmosphere  on  the  moon,  it  is  thought. 

MARS. — The  fourth  planet  of  the  system  has  a  year  of  about  687  days  ;  dis- 
tance from  sun,  141  million  miles  ;  diameter,  4,211  miles.  It  has  two  moons; 
day  about  the  same  as  ours  ;  orbital  speed,  900  miles  per  minute. 

JUPITER. — The  fifth  planet,  has  -)  moons  ;  distance,  480  million  miles  ;  vol- 
ume 1-1,000  that  of  sun.  His  days,  gh.  55m.  203.  He  has  four  satellites  ;  diam- 
eter, 86,000  miles.  His  year  equals  12  of  ours  ;  velocity,  483  miles  a  minute. 

SATURN. — Annual  revolution  around  the  sun  29*4  years  ;  distance  from  sun, 
SSi  million  miles ;  diameter,  70,500  miles  :  volume  700  times  that  of  Earth.  Den- 
sity, less  than  that  of  any  other  heavenly  body,  or  less  than  water.  Day,  loh. 
I4m.  243.  It  is  the  most  remarkable  planet  on  account  of  its  belt  and  8  satellites. 

URANUS. — Revolves  about  the  Sun  in  84  years  ;  diameter  50,000  kilometres ; 
has  two  known  satellites  ;  is  distant  from  sun  1,770,000,000  miles.  His  year  is 
84  of  ours. 

NEPTUNE. —Little  is  known  of  this  planet.  His  mean  distance  is  nearly 
3  billion  miles;  periodic  time,  164  years;  has  i  moon;  diameter,  55,000  kilo- 
metres, or  34,520  miles. 

The  air  roofs  us  over  and  retaining  the  heat  of  the  sun  keeps  us  warm.  The 
sun's  constant  force  displayed  on  the  earth,  is  equal  to  543  trillions  of  engines 
of  400  horse  power  each,  working  day  and  night  !  A  man  weighing  150  Ibs. 
on  earth,  weighs  396  on  Jupiter. 

Earth  is  3,236,000  miles  nearer  to  sun  in  winter  than  in  summer.  Hence  it  is 
hotter  in  the  summer  of  the  southern  hemisphere  than  in  the  northern  summer. 

SPACE  has  probably  no  resisting  medium  ;  its  temperature  is  about  200  de- 
grees below  zero. 

I..IGHT  goes  185,000  miles  a  second. 

The  nearest  fixed  star  is  16  billion  miles  distant,  and  it  takes  three  years  lor 
its  light  to  reach  us  !  The  highest  speed  of  a  rifle  ball  is  2,000  feet  per  second . 

The  diameters  of  the  asteroids  are  from  20  to  400  miles.  Mass  of  all  of 
them  put  together  less  than  one-quarter  of  earth. 

Arago  thinks  there  are  about  18  million  comets  traversing  our  system.  They 
are  thought  to  be  fluid  or  vapor. 

STARS. — There  are  about  5,000  visible  in  the  whole  heavens,  both  north  and 
south.  There  are  20  of  the  ist  magnitude,  65  of  the  2nd,  200  of  the  3rd,  400  of 
the  4th,  1,100  of  the  5th,  3,200  of  the  6th.  But  of  the  7th  magnitude  there  are 
13000  stars,  the  8th  40,000,  the  9th  142,000.  In  the  Milky  Way,  there  are  18 
million  stars,  and  when  we  consider  that  we  are  on  one  of  the  stars  of  the 
Milky  Way,  how  wonderful  the  works  of  creation,  and  how  insignificant,  rela- 
tively is  the  earth  ! 


School  Apparatus 


Of  all  kinds,  and  very  best  quality,  such  as  Globes  (60  kinds),  Blackboards, 
Liquid  Sla'ing1  for  same,  Outline  Maps,  Anatomical  and  Reading-  Charts,  Nu- 
meral Frames,  Andrews'  Slate  Drawing  Book,  Noiseless  Slates,  etc. 


Map  and  Blackboard  Pointers,  with  and  without  Lineal  Measures. 


No  Crayon  we  have  ever  been  compares  with  the  new  Alpha  Dustless. 
It  makes  a  clenn  white  mark,  is  not  greasy  and  does  not  scratch  the  board.  It 
outlasts  six  chalk  crayons .  The  demand  for  it  is  unprecedented.  Samples  sent 
teachers  on  application.  75c  per  gro-s.  5  gross  for  $3  50 


Dustless  Blackboard  Eraser. 


(Patented,) 


And  the  Best  Ever  Used.     Only  91.80  Per  Dozen. 

Sample  sent  on  receipt  of  150. 


It  is  enough  to  say  that^teachers  consider 
this  the  best  Eraser  for  the  price  they  have 
ever  tried,  :tnd  the  most  free  from  dust. 


The  cut  on  the  right  shows  the  Globe 
Case  which  is  sent  with  all  S  and  12  inch 
globes  It  may  be  hung  up  on  the  wall 
i  the  school  room  as  shown  in  cut,  or  closed 
and  locked  at  night. 

Our  new,  complete  and  handsomely  Illus- 
trated Catalogue  of  School  Merchandise 
will  be  mailed  any  one  on  receipt  of  20  cts. 

Address  for  all  particulars  the 

Manufacturers, 

A.  H.  Andrews  &  Co., 

195  and  197  Wabash  Ave.,  Chicago. 


The  Triumph  School  Desks. 


Dovetailed  and  Doweled  Together.     Both  Stationary 
and  Folding  Top. 

These  Desks,  of  such  acknowledged  superiority  in  construction  to  any  nml 
all  other  desks,  received  the  highest  awards  at  both  the  Philadelphia  and  Paris 
Expositions  !  This  meant  something  at  the  time,  and  it  means  something  still ! 

Educators  and  School  Officers  who  wish  to  know  the  requisites  of  a  first- 
class  desk,  and  WHY  the  TRIUMPH  has  and  must  continue  to  take  the  lead, 
will  please  send  for  our  Descriptive  Circulars  of  Desks  and  all  kinds  of  School 
Merchandise. 


The  New  Folding  Lid  Desks. 


The  lid  and  seat  are  folding  and  reduce  the  space  to  the  minimum.  The 
lid  assumes  four  positions.  Two  for  study,  one  for  writing  and  one  as  when 
closed  and  locked  upon  the  book  box. 

Address  the  Manufacturers, 

A.  H.  Andrews  &  Co., 

195  and  197  Wabash  Ave.,  Chicago,  111. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


SEP  28    933 

SEP  29  Wo 

REC'D  LD 

| 

OCT    3  1957 

LD21-100m-7,'33 

1 11 8ft  I 


